1
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Renner MJ. Compatibility of Generalized Noisy Qubit Measurements. PHYSICAL REVIEW LETTERS 2024; 132:250202. [PMID: 38996265 DOI: 10.1103/physrevlett.132.250202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Revised: 03/12/2024] [Accepted: 04/11/2024] [Indexed: 07/14/2024]
Abstract
It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine the critical visibility such that all qubit measurements, i.e., all positive operator-valued measures (POVMs), become compatible, i.e., jointly measurable. In addition, we apply our methods to quantum steering and Bell nonlocality. We obtain a tight local hidden state model for two-qubit Werner states of visibility 1/2. This determines the exact steering bound for two-qubit Werner states and also provides a local hidden variable model that improves on previously known models. Interestingly, this proves that POVMs are not more powerful than projective measurements to demonstrate quantum steering for these states.
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Affiliation(s)
- Martin J Renner
- University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ), Boltzmanngasse 5, 1090 Vienna, Austria and Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
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2
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Orsini DF, Oliveira LRN, da Luz MGE. Correlations in the EPR State Observables. ENTROPY (BASEL, SWITZERLAND) 2024; 26:476. [PMID: 38920485 PMCID: PMC11203292 DOI: 10.3390/e26060476] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Revised: 05/21/2024] [Accepted: 05/24/2024] [Indexed: 06/27/2024]
Abstract
The identification and physical interpretation of arbitrary quantum correlations are not always effortless. Two features that can significantly influence the dispersion of the joint observable outcomes in a quantum bipartite system composed of systems I and II are: (a) All possible pairs of observables describing the composite are equally probable upon measurement, and (b) The absence of concurrence (positive reinforcement) between any of the observables within a particular system; implying that their associated operators do not commute. The so-called EPR states are known to observe (a). Here, we demonstrate in very general (but straightforward) terms that they also satisfy condition (b), a relevant technical fact often overlooked. As an illustration, we work out in detail the three-level systems, i.e., qutrits. Furthermore, given the special characteristics of EPR states (such as maximal entanglement, among others), one might intuitively expect the CHSH correlation, computed exclusively for the observables of qubit EPR states, to yield values greater than two, thereby violating Bell's inequality. We show such a prediction does not hold true. In fact, the combined properties of (a) and (b) lead to a more limited range of values for the CHSH measure, not surpassing the nonlocality threshold of two. The present constitutes an instructive example of the subtleties of quantum correlations.
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Affiliation(s)
| | | | - Marcos G. E. da Luz
- Departamento de Física, Universidade Federal do Paraná, Curitiba 81531-980, Brazil; (D.F.O.); (L.R.N.O.)
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3
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Qu R, Zhang C, Chang ZH, Zhang XL, Guo Y, Hu XM, Li CF, Guo GC, Zhang P, Liu BH. Observation of Diverse Asymmetric Structures in High-Dimensional Einstein-Podolsky-Rosen Steering. PHYSICAL REVIEW LETTERS 2024; 132:210202. [PMID: 38856248 DOI: 10.1103/physrevlett.132.210202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Accepted: 04/22/2024] [Indexed: 06/11/2024]
Abstract
Einstein-Podolsky-Rosen (EPR) steering, a distinctive quantum correlation, reveals a unique and inherent asymmetry. This research delves into the multifaceted asymmetry of EPR steering within high-dimensional quantum systems, exploring both theoretical frameworks and experimental validations. We introduce the concept of genuine high-dimensional one-way steering, wherein a high Schmidt number of bipartite quantum states is demonstrable in one steering direction but not reciprocally. Additionally, we explore two criteria to certify the lower and upper bounds of the Schmidt number within a one-sided device-independent context. These criteria serve as tools for identifying potential asymmetric dimensionality of EPR steering in both directions. By preparing two-qutrit mixed states with high fidelity, we experimentally observe asymmetric structures of EPR steering in the C^{3}⊗C^{3} Hilbert space. Our Letter offers new perspectives to understand the asymmetric EPR steering beyond qubits and has potential applications in asymmetric high-dimensional quantum information tasks.
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Affiliation(s)
- Rui Qu
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ze-Hong Chang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Xiao-Lin Zhang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yu Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Pei Zhang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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4
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Villegas-Aguilar L, Polino E, Ghafari F, Quintino MT, Laverick KT, Berkman IR, Rogge S, Shalm LK, Tischler N, Cavalcanti EG, Slussarenko S, Pryde GJ. Nonlocality activation in a photonic quantum network. Nat Commun 2024; 15:3112. [PMID: 38600084 PMCID: PMC11006907 DOI: 10.1038/s41467-024-47354-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 03/28/2024] [Indexed: 04/12/2024] Open
Abstract
Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation. Nonlocality quickly deteriorates in the presence of noise, and restoring nonlocal correlations requires additional resources. These often come in the form of many instances of the input state and joint measurements, incurring a significant resource overhead. Here, we experimentally demonstrate that single copies of Bell-local states, incapable of violating any standard Bell inequality, can give rise to nonlocality after being embedded into a quantum network of multiple parties. We subject the initial entangled state to a quantum channel that broadcasts part of the state to two independent receivers and certify the nonlocality in the resulting network by violating a tailored Bell-like inequality. We obtain these results without making any assumptions about the prepared states, the quantum channel, or the validity of quantum theory. Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications, even in scenarios dominated by noise.
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Affiliation(s)
- Luis Villegas-Aguilar
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, QLD, 4111, Australia
| | - Emanuele Polino
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, QLD, 4111, Australia
| | - Farzad Ghafari
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, QLD, 4111, Australia
| | | | - Kiarn T Laverick
- Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, QLD, 4222, Australia
| | - Ian R Berkman
- Centre for Quantum Computation and Communication Technology, School of Physics, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - Sven Rogge
- Centre for Quantum Computation and Communication Technology, School of Physics, The University of New South Wales, Sydney, NSW, 2052, Australia
| | - Lynden K Shalm
- National Institute of Standards and Technology, 325 Broadway, Boulder, CO, 80305, USA
| | - Nora Tischler
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, QLD, 4111, Australia.
| | - Eric G Cavalcanti
- Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, QLD, 4222, Australia.
| | - Sergei Slussarenko
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, QLD, 4111, Australia
| | - Geoff J Pryde
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, QLD, 4111, Australia
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5
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Li Y, Xiang Y, Yu XD, Nguyen HC, Gühne O, He Q. Randomness Certification from Multipartite Quantum Steering for Arbitrary Dimensional Systems. PHYSICAL REVIEW LETTERS 2024; 132:080201. [PMID: 38457732 DOI: 10.1103/physrevlett.132.080201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2023] [Revised: 12/06/2023] [Accepted: 01/24/2024] [Indexed: 03/10/2024]
Abstract
Entanglement in bipartite systems has been applied to generate secure random numbers, which are playing an important role in cryptography or scientific numerical simulations. Here, we propose to use multipartite entanglement distributed between trusted and untrusted parties for generating randomness of arbitrary dimensional systems. We show that the distributed structure of several parties leads to additional protection against possible attacks by an eavesdropper, resulting in more secure randomness generated than in the corresponding bipartite scenario. Especially, randomness can be certified in the group of untrusted parties, even when there is no randomness in either of them individually. We prove that the necessary and sufficient resource for quantum randomness in this scenario is multipartite quantum steering when each untrusted party has a choice between only two measurements. However, the sufficiency no longer holds with more measurement settings. Finally, we apply our analysis to some experimentally realized states and show that more randomness can be extracted compared with the existing analysis.
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Affiliation(s)
- Yi Li
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Yu Xiang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Xiao-Dong Yu
- Department of Physics, Shandong University, Jinan 250100, China
| | - H Chau Nguyen
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Qiongyi He
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, Jiangsu, China
- Hefei National Laboratory, Hefei 230088, China
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6
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Tavakoli A. Quantum Steering with Imprecise Measurements. PHYSICAL REVIEW LETTERS 2024; 132:070204. [PMID: 38427889 DOI: 10.1103/physrevlett.132.070204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Accepted: 01/29/2024] [Indexed: 03/03/2024]
Abstract
We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. We show that small measurement imprecision can have a large detrimental influence in terms of false positives for steering inequalities, and that this effect can become even more relevant for high-dimensional systems. We then introduce a method for taking generic measurement imprecision into account in tests of bipartite steering inequalities. The revised steering bounds returned by this method are analytical, easily computable, and are even optimal for well-known families of arbitrary-dimensional steering tests. Furthermore, it applies equally well to generalized quantum steering scenarios, where the shared quantum state does not need to be separable, but is instead limited by some other entanglement property.
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Affiliation(s)
- Armin Tavakoli
- Physics Department, Lund University, Box 118, 22100 Lund, Sweden
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7
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Kadlec J, Bartkiewicz K, Černoch A, Lemr K, Miranowicz A. Experimental hierarchy of the nonclassicality of single-qubit states via potentials for entanglement, steering, and Bell nonlocality. OPTICS EXPRESS 2024; 32:2333-2346. [PMID: 38297766 DOI: 10.1364/oe.506169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 11/13/2023] [Indexed: 02/02/2024]
Abstract
Entanglement potentials are a promising way to quantify the nonclassicality of single-mode states. They are defined by the amount of entanglement (expressed by, e.g., the Wootters concurrence) obtained after mixing the examined single-mode state with a purely classical state; such as the vacuum or a coherent state. We generalize the idea of entanglement potentials to other quantum correlations: the EPR steering and Bell nonlocality, thus enabling us to study mutual hierarchies of these nonclassicality potentials. Instead of the usual vacuum and one-photon superposition states, we experimentally test this concept using specially tailored polarization-encoded single-photon states. One polarization encodes a given nonclassical single-mode state, while the other serves as the vacuum place-holder. This technique proves to be experimentally more convenient in comparison to the vacuum and a one-photon superposition as it does not require the vacuum detection.
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8
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Tendick L, Kampermann H, Bruß D. Distributed Quantum Incompatibility. PHYSICAL REVIEW LETTERS 2023; 131:120202. [PMID: 37802938 DOI: 10.1103/physrevlett.131.120202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Revised: 07/03/2023] [Accepted: 08/23/2023] [Indexed: 10/08/2023]
Abstract
Incompatible, i.e., nonjointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a measurement scheme. However, it is generally unclear how large this enhancement is and on what it depends. Here, we show that the incompatibility which is gained via additional measurements is upper and lower bounded by certain functions of the incompatibility of subsets of the available measurements. We prove the tightness of some of our bounds by providing explicit examples based on mutually unbiased bases. Finally, we discuss the consequences of our results for the nonlocality that can be gained by enlarging the number of measurements in a Bell experiment.
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Affiliation(s)
- Lucas Tendick
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hermann Kampermann
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany
| | - Dagmar Bruß
- Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany
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9
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Sekatski P, Giraud F, Uola R, Brunner N. Unlimited One-Way Steering. PHYSICAL REVIEW LETTERS 2023; 131:110201. [PMID: 37774268 DOI: 10.1103/physrevlett.131.110201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 07/20/2023] [Indexed: 10/01/2023]
Abstract
This work explores the asymmetry of quantum steering in a setup using high-dimensional entanglement. We construct entangled states with the following properties: (i) one party (Bob) can never steer the state of the other party (Alice), considering the most general measurements, and (ii) Alice can strongly steer the state of Bob, in the sense of demonstrating genuine high-dimensional steering. In other words, Alice can convince Bob that they share an entangled state of arbitrarily high Schmidt number, while Bob can never convince Alice that the state is even simply entangled. In this sense, one-way steering can become unlimited. A key result for our construction is a condition for the joint measurability of all high-dimensional measurements subjected to the combined effect of noise and loss, which is of independent interest.
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Affiliation(s)
- Pavel Sekatski
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Florian Giraud
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Roope Uola
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
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10
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Zahia AA, Abd-Rabbou MY, Megahed AM, Obada ASF. Bidirectional field-steering and atomic steering induced by a magnon mode in a qubit-photon system. Sci Rep 2023; 13:14943. [PMID: 37696940 PMCID: PMC10495356 DOI: 10.1038/s41598-023-41907-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 09/01/2023] [Indexed: 09/13/2023] Open
Abstract
This paper investigates the cavity-magnon steering and qubit-qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity-magnon steering and qubit-qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom-field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon-field coupling enhances and elevates the lower bounds of qubit-qubit steering. Further, adding the damping rates causes deterioration of the cavity-magnon steering and qubit-qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters.
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Affiliation(s)
- Ahmed A Zahia
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - M Y Abd-Rabbou
- Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt.
| | - Ahmed M Megahed
- Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
| | - A-S F Obada
- Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt
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11
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Abo S, Soubusta J, Jiráková K, Bartkiewicz K, Černoch A, Lemr K, Miranowicz A. Experimental hierarchy of two-qubit quantum correlations without state tomography. Sci Rep 2023; 13:8564. [PMID: 37237018 DOI: 10.1038/s41598-023-35015-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 05/11/2023] [Indexed: 05/28/2023] Open
Abstract
A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.
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Affiliation(s)
- Shilan Abo
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland
| | - Jan Soubusta
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic.
| | - Kateřina Jiráková
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic
| | - Karol Bartkiewicz
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic
| | - Antonín Černoch
- Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1154/50a, 779 00, Olomouc, Czech Republic
| | - Karel Lemr
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic
| | - Adam Miranowicz
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland.
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12
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Rahman AU, Abd‐Rabbou MY, Haddadi S, Ali H. Two‐Qubit Steerability, Nonlocality, and Average Steered Coherence under Classical Dephasing Channels. ANNALEN DER PHYSIK 2023; 535. [DOI: 10.1002/andp.202200523] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2022] [Indexed: 09/02/2023]
Abstract
AbstractWhen two qubits are prepared in a mixture of two Bell states and exposed to local transmission channels, the dynamics of steerability, Bell nonlocality, and average steered coherence are investigated. Disorders are assumed to influence the channels, resulting in either Markovian Ornstein–Uhlenbeck noise or non‐Markovian static noise in two models: a single noisy channel or two local noisy channels. Their findings show that the type and number of classical channels, noise, and initial state must be in an optimal setting in order to preserve quantum correlations.
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Affiliation(s)
- Atta ur Rahman
- School of Physics University of Chinese Academy of Science Yuquan Road 19A Beijing 100049 China
| | - M. Y. Abd‐Rabbou
- Mathematics Department Faculty of Science, Al‐Azhar University Nasr City Cairo 11884 Egypt
| | - Saeed Haddadi
- School of Physics Institute for Research in Fundamental Sciences (IPM) Tehran 19395‐5531 Iran
- Saeed's Quantum Information Group Tehran 19395‐0560 Iran
| | - Hazrat Ali
- Department of Physics Abbottabad University of Science and Technology Havellian KP 22500 Pakistan
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13
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Tong X, He Z, Zhang Y, Solomon S, Lin L, Song Q, Wang LV. Experimental full-domain mapping of quantum correlation in Clauser-Horne-Shimony-Holt scenarios. PHYSICAL REVIEW APPLIED 2023; 19:034049. [PMID: 38249539 PMCID: PMC10798678 DOI: 10.1103/physrevapplied.19.034049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/23/2024]
Abstract
Quantum correlation between two parties serves as an important resource in the surging applications of quantum information. The Bell nonlocality and quantum steering have been proposed to describe non-classical correlations against local-hidden-variable and local-hidden-state theories, respectively. To characterize the two types of non-classical correlations, various nonlocality and steering inequalities have been established, and the amount of inequality violation serves as an important indicator for many entanglement-based tasks. Quantum state tomography has been employed for measuring quantum states, while the method requires intensive computation and does not directly verify either nonlocality or steering over the full domain independent of established theories. Here, we experimentally map the full-domain correlation with bipartite states for nonlocality and quantum steering in CHSH scenarios. The measurement of the maps automatically accounts for detection imperfections. Furthermore, we demonstrate the application of the correlation maps in the entanglement-based quantum key distribution protocol with arbitrary bipartite states. The correlation maps show direct measurements and simple interpretations that can answer fundamental questions about nonlocality and quantum steering as well as contribute to quantum information applications in a straightforward manner.
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Affiliation(s)
| | | | | | - Samuel Solomon
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
| | - Li Lin
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
| | - Qiyuan Song
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
| | - Lihong V. Wang
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
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14
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Physical interpretation of nonlocal quantum correlation through local description of subsystems. Sci Rep 2022; 12:16400. [PMID: 36180489 PMCID: PMC9525634 DOI: 10.1038/s41598-022-17540-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2021] [Accepted: 07/27/2022] [Indexed: 11/08/2022] Open
Abstract
Characterization and categorization of quantum correlations are both fundamentally and practically important in quantum information science. Although quantum correlations such as non-separability, steerability, and non-locality can be characterized by different theoretical models in different scenarios with either known (trusted) or unknown (untrusted) knowledge of the associated systems, such characterization sometimes lacks unambiguous to experimentalist. In this work, we propose the physical interpretation of nonlocal quantum correlation between two systems. In the absence of complete local description of one of the subsystems quantified by the local uncertainty relation, the correlation between subsystems becomes nonlocal. Remarkably, different nonlocal quantum correlations can be discriminated from a single uncertainty relation derived under local hidden state (LHS)-LHS model only. We experimentally characterize the two-qubit Werner state in different scenarios.
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15
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Chen Z, Fei SM. Detecting Tripartite Steering via Quantum Entanglement. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1297. [PMID: 36141183 PMCID: PMC9497636 DOI: 10.3390/e24091297] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 09/09/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.
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Affiliation(s)
- Zhihua Chen
- School of Science, Jimei University, Xiamen 361021, China
| | - Shao-Ming Fei
- School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
- Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
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16
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Complete classification of steerability under local filters and its relation with measurement incompatibility. Nat Commun 2022; 13:4973. [PMID: 36008389 PMCID: PMC9411635 DOI: 10.1038/s41467-022-32466-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 07/18/2022] [Indexed: 11/16/2022] Open
Abstract
Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples. The study of quantum steering has both foundational and practical interest. Here, the authors show that transformability of a steerable resource into another via local filtering at the trusted party is determined by whether they have the same steering equivalent observables (SEO).
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17
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Alaoui YA, Zhu B, Muleady SR, Dubosclard W, Roscilde T, Rey AM, Laburthe-Tolra B, Vernac L. Measuring Correlations from the Collective Spin Fluctuations of a Large Ensemble of Lattice-Trapped Dipolar Spin-3 Atoms. PHYSICAL REVIEW LETTERS 2022; 129:023401. [PMID: 35867449 DOI: 10.1103/physrevlett.129.023401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Revised: 03/23/2022] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
We perform collective spin measurements to study the buildup of two-body correlations between ≈10^{4} spin s=3 chromium atoms pinned in a 3D optical lattice. The spins interact via long range and anisotropic dipolar interactions. From the fluctuations of total magnetization, measured at the standard quantum limit, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. The quantum nature of the correlations is assessed by comparisons with analytical short- and long-time expansions and numerical simulations. Our Letter shows that measuring fluctuations of spin populations for s>1/2 spins provides new ways to characterize correlations in quantum many-body systems.
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Affiliation(s)
- Youssef Aziz Alaoui
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Bihui Zhu
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA and Center for Quantum Research and Technology, The University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Sean Robert Muleady
- JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - William Dubosclard
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Tommaso Roscilde
- Université Lyon, Ens de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Ana Maria Rey
- JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Bruno Laburthe-Tolra
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Laurent Vernac
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
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18
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Qu R, Wang Y, An M, Wang F, Quan Q, Li H, Gao H, Li F, Zhang P. Retrieving High-Dimensional Quantum Steering from a Noisy Environment with N Measurement Settings. PHYSICAL REVIEW LETTERS 2022; 128:240402. [PMID: 35776453 DOI: 10.1103/physrevlett.128.240402] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 08/03/2021] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
One of the most often implied benefits of high-dimensional (HD) quantum systems is to lead to stronger forms of correlations, featuring increased robustness to noise. Here, we experimentally demonstrate the n-setting linear HD quantum steering criterion. We verify the large violation of the steering inequalities without full-state tomography. The lower bound of the violation is 2.24±0.01 in 11 dimensions, exceeding the bound (V<2) of two-setting criteria. Hence, a higher strength of steering has been revealed. Moreover, we demonstrate the method for enhancing the noise robustness without increasing dimension, alternatively, by increasing measurement settings. Using the entanglement in 11 dimensions, we experimentally retrieve steering nonlocality with 63.4±1.4% isotropic noise fraction, surpassing the 50% limitation of two-setting criteria. Our Letter offers the potential for practical one-sided device-independent quantum information processing that tolerates the noisy environment, lossy detection, and transcends the present transmission distance limitation.
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Affiliation(s)
- Rui Qu
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yunlong Wang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Min An
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Feiran Wang
- School of Science, Xi'an Polytechnic University, Xi'an 710048, China
| | - Quan Quan
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Hongrong Li
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Hong Gao
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Fuli Li
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Pei Zhang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Shaanxi Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
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19
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Liu S, Han D, Wang N, Xiang Y, Sun F, Wang M, Qin Z, Gong Q, Su X, He Q. Experimental Demonstration of Remotely Creating Wigner Negativity via Quantum Steering. PHYSICAL REVIEW LETTERS 2022; 128:200401. [PMID: 35657859 DOI: 10.1103/physrevlett.128.200401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Revised: 02/16/2022] [Accepted: 04/21/2022] [Indexed: 06/15/2023]
Abstract
Non-Gaussian states with Wigner negativity are of particular interest in quantum technology due to their potential applications in quantum computing and quantum metrology. However, how to create such states at a remote location remains a challenge, which is important for efficiently distributing quantum resource between distant nodes in a network. Here, we experimentally prepare an optical non-Gaussian state with negative Wigner function at a remote node via local non-Gaussian operation and shared Gaussian entangled state existing quantum steering. By performing photon subtraction on one mode, Wigner negativity is created in the remote target mode. We show that the Wigner negativity is sensitive to loss on the target mode, but robust to loss on the mode performing photon subtraction. This experiment confirms the connection between the remotely created Wigner negativity and quantum steering. As an application, we present that the generated non-Gaussian state exhibits metrological power in quantum phase estimation.
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Affiliation(s)
- Shuheng Liu
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
| | - Dongmei Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Na Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yu Xiang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Fengxiao Sun
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Meihong Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Zhongzhong Qin
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, Jiangsu, China
| | - Xiaolong Su
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Qiongyi He
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, Jiangsu, China
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20
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Hao ZY, Sun K, Wang Y, Liu ZH, Yang M, Xu JS, Li CF, Guo GC. Demonstrating Shareability of Multipartite Einstein-Podolsky-Rosen Steering. PHYSICAL REVIEW LETTERS 2022; 128:120402. [PMID: 35394318 DOI: 10.1103/physrevlett.128.120402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 04/19/2021] [Accepted: 03/03/2022] [Indexed: 06/14/2023]
Abstract
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.
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Affiliation(s)
- Ze-Yan Hao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Kai Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yan Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zheng-Hao Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Mu Yang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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21
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Jones BDM, Šupić I, Uola R, Brunner N, Skrzypczyk P. Network Quantum Steering. PHYSICAL REVIEW LETTERS 2021; 127:170405. [PMID: 34739296 DOI: 10.1103/physrevlett.127.170405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Accepted: 09/02/2021] [Indexed: 06/13/2023]
Abstract
The development of large-scale quantum networks promises to bring a multitude of technological applications as well as shed light on foundational topics, such as quantum nonlocality. It is particularly interesting to consider scenarios where sources within the network are statistically independent, which leads to so-called network nonlocality, even when parties perform fixed measurements. Here we promote certain parties to be trusted and introduce the notion of network steering and network local hidden state (NLHS) models within this paradigm of independent sources. In one direction, we show how the results from Bell nonlocality and quantum steering can be used to demonstrate network steering. We further show that it is a genuinely novel effect by exhibiting unsteerable states that nevertheless demonstrate network steering based upon entanglement swapping yielding a form of activation. On the other hand, we provide no-go results for network steering in a large class of scenarios by explicitly constructing NLHS models.
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Affiliation(s)
- Benjamin D M Jones
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
- Quantum Engineering Centre for Doctoral Training, University of Bristol, Bristol BS8 1FD, United Kingdom
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Ivan Šupić
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
- CNRS, LIP6, Sorbonne Université, 4 Place Jussieu, 75005 Paris, France
| | - Roope Uola
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Paul Skrzypczyk
- H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
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22
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Riedel Gårding E, Schwaller N, Chan CL, Chang SY, Bosch S, Gessler F, Laborde WR, Hernandez JN, Si X, Dupertuis MA, Macris N. Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer. ENTROPY (BASEL, SWITZERLAND) 2021; 23:797. [PMID: 34201581 PMCID: PMC8304312 DOI: 10.3390/e23070797] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Revised: 06/16/2021] [Accepted: 06/17/2021] [Indexed: 11/17/2022]
Abstract
We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between "quantum discord" and "asymmetric relative entropy of discord": the former never exceeds the latter. We also prove that for all BDS the two coincide.
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Affiliation(s)
- Elias Riedel Gårding
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
- Department of Physics, Royal Institute of Technology (KTH), 100 44 Stockholm, Sweden
| | - Nicolas Schwaller
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
| | - Chun Lam Chan
- Laboratoire de Théorie des Communications, Faculté Informatique et Communications, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (C.L.C.); (F.G.)
| | - Su Yeon Chang
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
| | - Samuel Bosch
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
| | - Frederic Gessler
- Laboratoire de Théorie des Communications, Faculté Informatique et Communications, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (C.L.C.); (F.G.)
| | - Willy Robert Laborde
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
- School of Physics, AMBER and CRANN Institute, Trinity College Dublin, The University of Dublin, College Green, Dublin 2, Ireland
| | - Javier Naya Hernandez
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
- School of Science and Engineering, Tecnológico de Monterrey, Monterrey 64849, Mexico
| | - Xinyu Si
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
| | - Marc-André Dupertuis
- Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (E.R.G.); (N.S.); (S.Y.C.); (S.B.); (W.R.L.); (J.N.H.); (X.S.)
| | - Nicolas Macris
- Laboratoire de Théorie des Communications, Faculté Informatique et Communications, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; (C.L.C.); (F.G.)
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23
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Designolle S, Srivastav V, Uola R, Valencia NH, McCutcheon W, Malik M, Brunner N. Genuine High-Dimensional Quantum Steering. PHYSICAL REVIEW LETTERS 2021; 126:200404. [PMID: 34110189 DOI: 10.1103/physrevlett.126.200404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 04/01/2021] [Accepted: 04/15/2021] [Indexed: 06/12/2023]
Abstract
High-dimensional quantum entanglement can give rise to stronger forms of nonlocal correlations compared to qubit systems, offering significant advantages for quantum information processing. Certifying these stronger correlations, however, remains an important challenge, in particular in an experimental setting. Here we theoretically formalize and experimentally demonstrate a notion of genuine high-dimensional quantum steering. We show that high-dimensional entanglement, as quantified by the Schmidt number, can lead to a stronger form of steering, provably impossible to obtain via entanglement in lower dimensions. Exploiting the connection between steering and incompatibility of quantum measurements, we derive simple two-setting steering inequalities, the violation of which guarantees the presence of genuine high-dimensional steering, and hence certifies a lower bound on the Schmidt number in a one-sided device-independent setting. We report the experimental violation of these inequalities using macropixel photon-pair entanglement certifying genuine high-dimensional steering. In particular, using an entangled state in dimension d=31, our data certifies a minimum Schmidt number of n=15.
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Affiliation(s)
| | - Vatshal Srivastav
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Roope Uola
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
| | - Natalia Herrera Valencia
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Will McCutcheon
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Mehul Malik
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Nicolas Brunner
- Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
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24
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Yadin B, Fadel M, Gessner M. Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox. Nat Commun 2021; 12:2410. [PMID: 33893281 PMCID: PMC8065158 DOI: 10.1038/s41467-021-22353-3] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 03/11/2021] [Indexed: 02/02/2023] Open
Abstract
The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.
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Affiliation(s)
- Benjamin Yadin
- grid.4563.40000 0004 1936 8868School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, UK ,grid.4991.50000 0004 1936 8948Wolfson College, University of Oxford, Oxford, UK
| | - Matteo Fadel
- grid.6612.30000 0004 1937 0642Department of Physics, University of Basel, Basel, Switzerland
| | - Manuel Gessner
- grid.462844.80000 0001 2308 1657Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, Paris, France
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25
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Chen Y, Zhang YL, Shen Z, Zou CL, Guo GC, Dong CH. Synthetic Gauge Fields in a Single Optomechanical Resonator. PHYSICAL REVIEW LETTERS 2021; 126:123603. [PMID: 33834826 DOI: 10.1103/physrevlett.126.123603] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 02/26/2021] [Indexed: 06/12/2023]
Abstract
Synthetic gauge fields have recently emerged, arising in the context of quantum simulations, topological matter, and the protected transportation of excitations against defects. For example, an ultracold atom experiences a light-induced effective magnetic field when tunneling in an optical lattice, and offering a platform to simulate the quantum Hall effect and topological insulators. Similarly, the magnetic field associated with photon transport between sites has been demonstrated in a coupled resonator array. Here, we report the first experimental demonstration of a synthetic gauge field in the virtual lattices of bosonic modes in a single optomechanical resonator. By employing degenerate clockwise and counterclockwise optical modes and a mechanical mode, a controllable synthetic gauge field is realized by tuning the phase of the driving lasers. The nonreciprocal conversion between the three modes is realized for different synthetic magnetic fluxes. As a proof-of-principle demonstration, we also show the dynamics of the system under a fast-varying synthetic gauge field, and demonstrate synthetic electric field. Our demonstration not only provides a versatile and controllable platform for studying synthetic gauge fields in high dimensions but also enables an exploration of ultrafast gauge field tuning with a large dynamic range, which is restricted for a magnetic field.
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Affiliation(s)
- Yuan Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Yan-Lei Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Zhen Shen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Chang-Ling Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Chun-Hua Dong
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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26
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Wang M, Xiang Y, Kang H, Han D, Liu Y, He Q, Gong Q, Su X, Peng K. Deterministic Distribution of Multipartite Entanglement and Steering in a Quantum Network by Separable States. PHYSICAL REVIEW LETTERS 2020; 125:260506. [PMID: 33449714 DOI: 10.1103/physrevlett.125.260506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 12/09/2020] [Indexed: 06/12/2023]
Abstract
As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.
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Affiliation(s)
- Meihong Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yu Xiang
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Haijun Kang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Dongmei Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yang Liu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Qiongyi He
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Qihuang Gong
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Xiaolong Su
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Kunchi Peng
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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27
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Nguyen HC, Gühne O. Some Quantum Measurements with Three Outcomes Can Reveal Nonclassicality where All Two-Outcome Measurements Fail to Do So. PHYSICAL REVIEW LETTERS 2020; 125:230402. [PMID: 33337196 DOI: 10.1103/physrevlett.125.230402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Revised: 09/03/2020] [Accepted: 10/21/2020] [Indexed: 06/12/2023]
Abstract
Measurements serve as the intermediate communication layer between the quantum world and our classical perception. So, the question of which measurements efficiently extract information from quantum systems is of central interest. Using quantum steering as a nonclassical phenomenon, we show that there are instances where the results of all two-outcome measurements can be explained in a classical manner, while the results of some three-outcome measurements cannot. This points to the important role of the number of outcomes in revealing the nonclassicality hidden in a quantum system. Moreover, our methods allow us to improve the understanding of quantum correlations by delivering novel criteria for quantum steering and improved ways to construct local hidden variable models.
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Affiliation(s)
- H Chau Nguyen
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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28
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Geometric quantum discord of Heisenberg model with dissipative terms. Sci Rep 2020; 10:10817. [PMID: 32616750 PMCID: PMC7331676 DOI: 10.1038/s41598-020-67698-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Accepted: 06/12/2020] [Indexed: 11/08/2022] Open
Abstract
AbstractIn this paper, we study a system with two interacting qubits described by the Heisenberg model with dissipative terms, and analyze decay dynamics and the steady-state of geometric quantum discords. Our results indicate that we can ignore the interaction force in the z-direction and adjust the parameters to change the loss of quantum correlation with time when the initial state satisfies some conditions. Moreover, we show that after a long enough period of time, unlike other parameters, the energy and the intensity of the non-uniform magnetic field do not affect the steady-state.
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29
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Rosset D, Schmid D, Buscemi F. Type-Independent Characterization of Spacelike Separated Resources. PHYSICAL REVIEW LETTERS 2020; 125:210402. [PMID: 33274994 DOI: 10.1103/physrevlett.125.210402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2020] [Accepted: 09/03/2020] [Indexed: 06/12/2023]
Abstract
Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in quantum networks. Not all such objects are useful, however. In the context of spacelike separated parties, devices which can be simulated using local operations and shared randomness are useless, and it is of paramount importance to be able to practically distinguish useful from useless quantum resources. Accordingly, a body of literature has arisen to provide tools for witnessing and quantifying the nonclassicality of objects of each specific type. In the present Letter, we provide a framework which subsumes and generalizes all of these resources, as well as the tools for witnessing and quantifying their nonclassicality.
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Affiliation(s)
- Denis Rosset
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
| | - David Schmid
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada and Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L3G1, Canada
| | - Francesco Buscemi
- Graduate School of Informatics, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan
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30
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Bernards F, Gühne O. Generalizing Optimal Bell Inequalities. PHYSICAL REVIEW LETTERS 2020; 125:200401. [PMID: 33258662 DOI: 10.1103/physrevlett.125.200401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Accepted: 10/12/2020] [Indexed: 06/12/2023]
Abstract
Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational complexity of characterizing the set of local correlations. We develop a method to characterize Bell inequalities under constraints, which may be given by symmetry or other linear conditions. This allows one to search systematically for generalizations of given Bell inequalities to more parties. As an example, we find all possible generalizations of the two-particle inequality by Froissart [Nuovo Cimento Soc. Ital. Fis. B 64, 241 (1981)], also known as I3322 inequality, to three particles. For the simplest of these inequalities, we study their quantum mechanical properties and demonstrate that they are relevant, in the sense that they detect nonlocality of quantum states, for which all two-setting inequalities fail to do so.
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Affiliation(s)
- Fabian Bernards
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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31
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Åberg J, Nery R, Duarte C, Chaves R. Semidefinite Tests for Quantum Network Topologies. PHYSICAL REVIEW LETTERS 2020; 125:110505. [PMID: 32975959 DOI: 10.1103/physrevlett.125.110505] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2020] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
Quantum networks play a major role in long-distance communication, quantum cryptography, clock synchronization, and distributed quantum computing. Generally, these protocols involve many independent sources sharing entanglement among distant parties that, upon measuring their systems, generate correlations across the network. The question of which correlations a given quantum network can give rise to remains almost uncharted. Here we show that constraints on the observable covariances, previously derived for the classical case, also hold for quantum networks. The network topology yields tests that can be cast as semidefinite programs, thus allowing for the efficient characterization of the correlations in a wide class of quantum networks, as well as systematic derivations of device-independent and experimentally testable witnesses. We obtain such semidefinite tests for fixed measurement settings, as well as parties that independently choose among collections of measurement settings. The applicability of the method is demonstrated for various networks, and compared with previous approaches.
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Affiliation(s)
- Johan Åberg
- Institute for Theoretical Physics, University of Cologne, Zülpicher Strasse 77, D-50937 Cologne, Germany
| | - Ranieri Nery
- International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
| | - Cristhiano Duarte
- Schmid College of Science and Technology, Chapman University, 1 University Drive, Orange, California 92866, USA
| | - Rafael Chaves
- International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
- School of Science and Technology, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil
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32
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Sainz AB, Hoban MJ, Skrzypczyk P, Aolita L. Bipartite Postquantum Steering in Generalized Scenarios. PHYSICAL REVIEW LETTERS 2020; 125:050404. [PMID: 32794874 DOI: 10.1103/physrevlett.125.050404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Revised: 02/18/2020] [Accepted: 06/29/2020] [Indexed: 06/11/2023]
Abstract
The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bob's system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the "instrumental steering" scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios.
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Affiliation(s)
- Ana Belén Sainz
- International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5
| | - Matty J Hoban
- Department of Computing, Goldsmiths, University of London, London SE14 6NW, United Kingdom
| | - Paul Skrzypczyk
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Leandro Aolita
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ, Brazil
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33
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Wollmann S, Uola R, Costa ACS. Experimental Demonstration of Robust Quantum Steering. PHYSICAL REVIEW LETTERS 2020; 125:020404. [PMID: 32701336 DOI: 10.1103/physrevlett.125.020404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Revised: 05/06/2020] [Accepted: 06/18/2020] [Indexed: 06/11/2023]
Abstract
We analyze and experimentally demonstrate quantum steering using criteria based on generalized entropies and criteria with minimal assumptions based on the so-called dimension-bounded steering. Further, we investigate and compare their robustness against experimental imperfections such as misalignment in the shared measurement reference frame. While entropy based criteria are robust against imperfections in state preparation, we demonstrate an advantage in dimension-bounded steering in the presence of measurement imprecision. As steering with such minimal assumptions is easier to reach than fully nonlocal correlations, and as our setting requires very little trust in the measurement devices, the results provide a candidate for the costly Bell tests while remaining highly device independent.
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Affiliation(s)
- Sabine Wollmann
- Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1FD, United Kingdom
- Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Roope Uola
- Département de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
| | - Ana C S Costa
- Department of Physics, Federal University of Paraná, 81531-980 Curitiba, PR, Brazil
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34
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Nery RV, Taddei MM, Sahium P, Walborn SP, Aolita L, Aguilar GH. Distillation of Quantum Steering. PHYSICAL REVIEW LETTERS 2020; 124:120402. [PMID: 32281831 DOI: 10.1103/physrevlett.124.120402] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Revised: 10/31/2019] [Accepted: 02/13/2020] [Indexed: 06/11/2023]
Abstract
We show-both theoretically and experimentally-that Einstein-Podolsky-Rosen steering can be distilled. We present a distillation protocol that outputs a perfectly correlated system-the singlet assemblage-in the asymptotic infinite-copy limit, even for inputs that are arbitrarily close to being unsteerable. As figures of merit for the protocol's performance, we introduce the assemblage fidelity and the singlet-assemblage fraction. These are potentially interesting quantities on their own beyond the current scope. Remarkably, the protocol works well also in the nonasymptotic regime of few copies, in the sense of increasing the singlet-assemblage fraction. We demonstrate the efficacy of the protocol using a hyperentangled photon pair encoding two copies of a two-qubit state. This represents to our knowledge the first observation of deterministic steering concentration. Our findings are not only fundamentally important but may also be useful for semi-device-independent protocols in noisy quantum networks.
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Affiliation(s)
- R V Nery
- Instituto de Física, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - M M Taddei
- Instituto de Física, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - P Sahium
- Instituto de Física, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - S P Walborn
- Instituto de Física, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - L Aolita
- Instituto de Física, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
| | - G H Aguilar
- Instituto de Física, Universidade Federal do Rio de Janeiro, P. O. Box 68528, Rio de Janeiro, Rio de Janeiro 21941-972, Brazil
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35
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Radhakrishnan C, Laurière M, Byrnes T. Multipartite Generalization of Quantum Discord. PHYSICAL REVIEW LETTERS 2020; 124:110401. [PMID: 32242682 DOI: 10.1103/physrevlett.124.110401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2019] [Revised: 02/12/2020] [Accepted: 02/12/2020] [Indexed: 06/11/2023]
Abstract
A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.
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Affiliation(s)
- Chandrashekar Radhakrishnan
- New York University Shanghai, 1555 Century Avenue, Pudong, Shanghai 200122, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Laboratoire Systèmes Complexes et Information Quantique, ESIEA Group, 9 Rue Vèsale, Paris 75005, France
| | - Mathieu Laurière
- New York University Shanghai, 1555 Century Avenue, Pudong, Shanghai 200122, China
- Princeton University, ORFE Department, 98 Charlton Street, Princeton, New Jersey 08540, USA
| | - Tim Byrnes
- New York University Shanghai, 1555 Century Avenue, Pudong, Shanghai 200122, China
- NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
- National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
- Department of Physics, New York University, New York, New York 10003, USA
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36
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Sadia Qureshi H, Ullah S, Ghafoor F. Bipartite Gaussian quantum steering, entanglement, and discord and their interconnection via a parametric down-converter. APPLIED OPTICS 2020; 59:2701-2708. [PMID: 32225818 DOI: 10.1364/ao.378891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 02/18/2020] [Indexed: 06/10/2023]
Abstract
In this study, we quantify quantum steering, quantum entanglement, and quantum discord and their interconnection using the technique of parametric down-conversion. Initially, two single-mode Gaussian states together with a non-linear crystal in a cavity are considered. The behavior of the three kinds of quantum correlations depend on the phase of the coherent pump field, purity, and non-classicality of the input states, and the damping rates of the cavity. The amount and time evolution of the quantum correlations enhances with the difference between the non-classicality of the initial states. In presence of the damping rates, the quantum steering and quantum entanglement (quantum discord) increase (decreases) with the purity of the input cavity field. We note that the amount and survival time of the quantum correlations can be controlled by varying the relative phase associated to the coherent pump field. The boundaries of the three kinds of quantum correlations are defined and explained with respect to each other, which form a hierarchy.
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37
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Tendick L, Kampermann H, Bruß D. Activation of Nonlocality in Bound Entanglement. PHYSICAL REVIEW LETTERS 2020; 124:050401. [PMID: 32083890 DOI: 10.1103/physrevlett.124.050401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Revised: 09/26/2019] [Accepted: 01/10/2020] [Indexed: 06/10/2023]
Abstract
We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully biseparable three-qubit bound entangled state with a local model for the most general (nonsequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters are applied. Our results demonstrate the first example of activation of nonlocality in bound entanglement. Hence, we show that genuine hidden nonlocality does not imply entanglement distillability.
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Affiliation(s)
- Lucas Tendick
- Institute for Theoretical Physics III, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Hermann Kampermann
- Institute for Theoretical Physics III, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Dagmar Bruß
- Institute for Theoretical Physics III, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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38
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Sun BZ, Wang ZX, Li-Jost X, Fei SM. A Note on the Hierarchy of Quantum Measurement Incompatibilities. ENTROPY 2020; 22:e22020161. [PMID: 33285936 PMCID: PMC7516579 DOI: 10.3390/e22020161] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 01/12/2020] [Revised: 01/26/2020] [Accepted: 01/27/2020] [Indexed: 11/16/2022]
Abstract
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, we present a complete classification of the incompatibility of a given measurement assemblage with n members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program.
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Affiliation(s)
- Bao-Zhi Sun
- School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
| | - Zhi-Xi Wang
- School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
| | - Xianqing Li-Jost
- Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
| | - Shao-Ming Fei
- School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
- Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany
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39
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Abstract
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e., we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
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40
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Liu Y, Cai Y, Xiang Y, Li F, Zhang Y, He Q. Tripartite Einstein-Podolsky-Rosen steering with linear and nonlinear beamsplitters in four-wave mixing of Rubidium atoms. OPTICS EXPRESS 2019; 27:33070-33079. [PMID: 31878381 DOI: 10.1364/oe.27.033070] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 10/13/2019] [Indexed: 06/10/2023]
Abstract
Multipartite Einstein-Podolsky-Rosen (EPR) steering is an essential resource for secure one-sided device-independent quantum secret sharing. Here, we analyze the EPR steering properties exhibited in three-mode Gaussian states created by four-wave mixing (FWM) in Rubidium atoms combined with a linear beamsplitter and a nonlinear beamsplitter (second FWM), respectively. By quantifying Gaussian steerability based on a measure determined by the covariance matrix of the produced states, we compare the performance of two schemes to achieve one-way, collective, and genuine tripartite steering, as well as the monogamy constraints for distributing steering among three parties. We show that the scheme with nonlinear beamsplitter is feasible to create stronger bipartite steering and genuine tripartite steering and has more flexibility to manipulate the monogamy relation through the cooperation of the two cascaded FWM processes.
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41
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Yang M, Ren CL, Ma YC, Xiao Y, Ye XJ, Song LL, Xu JS, Yung MH, Li CF, Guo GC. Experimental Simultaneous Learning of Multiple Nonclassical Correlations. PHYSICAL REVIEW LETTERS 2019; 123:190401. [PMID: 31765183 DOI: 10.1103/physrevlett.123.190401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Revised: 07/15/2019] [Indexed: 06/10/2023]
Abstract
Nonclassical correlations can be regarded as resources for quantum information processing. However, the classification problem of nonclassical correlations for quantum states remains a challenge, even for finite-size systems. Although there exists a set of criteria for determining individual nonclassical correlations, a unified framework that is capable of simultaneously classifying multiple correlations is still missing. In this Letter, we experimentally explored the possibility of applying machine-learning methods for simultaneously identifying nonclassical correlations. Specifically, by using partial information, we applied an artificial neural network, support vector machine, and decision tree for learning entanglement, quantum steering, and nonlocality. Overall, we found that, for a family of quantum states, all three approaches can achieve high accuracy for the classification problem. Moreover, the run time of the machine-learning methods to output the state label is experimentally found to be significantly less than that of state tomography.
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Affiliation(s)
- Mu Yang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chang-Liang Ren
- Center for Nanofabrication and System Integration, Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, People's Republic of China
| | - Yue-Chi Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
| | - Ya Xiao
- Department of Physics, Ocean University of China, Qingdao 266100, People's Republic of China
| | - Xiang-Jun Ye
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Lu-Lu Song
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Man-Hong Yung
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
- Central Research Institute, Huawei Technologies, Shenzhen 518129, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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Quintino MT, Budroni C, Woodhead E, Cabello A, Cavalcanti D. Device-Independent Tests of Structures of Measurement Incompatibility. PHYSICAL REVIEW LETTERS 2019; 123:180401. [PMID: 31763882 DOI: 10.1103/physrevlett.123.180401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2019] [Revised: 07/18/2019] [Indexed: 06/10/2023]
Abstract
In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell nonlocality. This makes it of crucial importance to develop tools for certifying whether a set of measurements respects a certain structure of incompatibility. Here we show that, for quantum or nonsignaling models, if the measurements employed in a Bell test satisfy a given type of compatibility, then the amount of violation of some specific Bell inequalities becomes limited. Then, we show that correlations arising from local measurements on two-qubit states violate these limits, which rules out in a device-independent way such structures of incompatibility. In particular, we prove that quantum correlations allow for a device-independent demonstration of genuine triplewise incompatibility. Finally, we translate these results into a semidevice-independent Einstein-Podolsky-Rosen-steering scenario.
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Affiliation(s)
- Marco Túlio Quintino
- Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Costantino Budroni
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Erik Woodhead
- ICFO-Institut de Ciències Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Daniel Cavalcanti
- ICFO-Institut de Ciències Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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43
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Guo Y, Cheng S, Hu X, Liu BH, Huang EM, Huang YF, Li CF, Guo GC, Cavalcanti EG. Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits. PHYSICAL REVIEW LETTERS 2019; 123:170402. [PMID: 31702255 DOI: 10.1103/physrevlett.123.170402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Revised: 09/24/2019] [Indexed: 06/10/2023]
Abstract
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for trusting a party is substituted by a quantum channel between the referee and that party, through which the referee encodes the measurements to be performed on that party's subsystem in a set of nonorthogonal quantum states. In this Letter, an EPR-steering inequality is adapted as a quantum-refereed EPR-steering witness, and the trust-free experimental verification of higher dimensional quantum steering is reported via preparing a class of entangled photonic qutrits. Further, with two measurement settings, we extract 1.106±0.023 bits of private randomness per every photon pair from our observed data, which surpasses the one-bit limit for projective measurements performed on qubit systems. Our results advance research on quantum information processing tasks beyond qubits.
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Affiliation(s)
- Yu Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Shuming Cheng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
| | - Xiaomin Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - En-Ming Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Eric G Cavalcanti
- Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Gold Coast, Queensland 4222, Australia
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Bharti K, Ray M, Varvitsiotis A, Warsi NA, Cabello A, Kwek LC. Robust Self-Testing of Quantum Systems via Noncontextuality Inequalities. PHYSICAL REVIEW LETTERS 2019; 122:250403. [PMID: 31347894 DOI: 10.1103/physrevlett.122.250403] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2019] [Revised: 06/03/2019] [Indexed: 06/10/2023]
Abstract
Characterizing unknown quantum states and measurements is a fundamental problem in quantum information processing. In this Letter, we provide a novel scheme to self-test local quantum systems using noncontextuality inequalities. Our work leverages the graph-theoretic framework for contextuality introduced by Cabello, Severini, and Winter, combined with tools from mathematical optimization that guarantee the unicity of optimal solutions. As an application, we show that the celebrated Klyachko-Can-Binicioğlu-Shumovsky inequality and its generalization to contextuality scenarios with odd n-cycle compatibility relations admit robust self-testing.
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Affiliation(s)
- Kishor Bharti
- Centre for Quantum Technologies, National University of Singapore 117543, Singapore
| | - Maharshi Ray
- Centre for Quantum Technologies, National University of Singapore 117543, Singapore
| | - Antonios Varvitsiotis
- Department of Electrical & Computer Engineering, National University of Singapore 117583, Singapore
| | - Naqueeb Ahmad Warsi
- Centre for Quantum Technologies, National University of Singapore 117543, Singapore
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Leong-Chuan Kwek
- Centre for Quantum Technologies, National University of Singapore 117543, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654, Singapore
- National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore
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45
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Nguyen HC, Nguyen HV, Gühne O. Geometry of Einstein-Podolsky-Rosen Correlations. PHYSICAL REVIEW LETTERS 2019; 122:240401. [PMID: 31322372 DOI: 10.1103/physrevlett.122.240401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2018] [Revised: 04/17/2019] [Indexed: 06/10/2023]
Abstract
Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications such as quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky, and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalize their argument, Schrödinger subsequently introduced the notion of quantum steering. Still, the question of which quantum states can be used for EPR steering and which cannot remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-1/2 particles, this approach completely characterizes the set of states leading to EPR steering. In addition, we discuss the generalization to higher-dimensional systems as well as generalized measurements. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question of which observables in quantum mechanics are jointly measurable.
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Affiliation(s)
- H Chau Nguyen
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Huy-Viet Nguyen
- Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi, Vietnam
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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46
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Zhen YZ, Xu XY, Li L, Liu NL, Chen K. The Einstein-Podolsky-Rosen Steering and Its Certification. ENTROPY 2019; 21:e21040422. [PMID: 33267136 PMCID: PMC7514909 DOI: 10.3390/e21040422] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2019] [Revised: 04/03/2019] [Accepted: 04/16/2019] [Indexed: 11/16/2022]
Abstract
The Einstein–Podolsky–Rosen (EPR) steering is a subtle intermediate correlation between entanglement and Bell nonlocality. It not only theoretically completes the whole picture of non-local effects but also practically inspires novel quantum protocols in specific scenarios. However, a verification of EPR steering is still challenging due to difficulties in bounding unsteerable correlations. In this survey, the basic framework to study the bipartite EPR steering is discussed, and general techniques to certify EPR steering correlations are reviewed.
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Affiliation(s)
- Yi-Zheng Zhen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Institute for Quantum Science and Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
| | - Xin-Yu Xu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Correspondence: (L.L.); (N.-L.L.); (K.C.)
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Correspondence: (L.L.); (N.-L.L.); (K.C.)
| | - Kai Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Correspondence: (L.L.); (N.-L.L.); (K.C.)
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47
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Gisin N. Entanglement 25 Years after Quantum Teleportation: Testing Joint Measurements in Quantum Networks. ENTROPY 2019; 21:e21030325. [PMID: 33267039 PMCID: PMC7514809 DOI: 10.3390/e21030325] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Revised: 03/15/2019] [Accepted: 03/20/2019] [Indexed: 11/16/2022]
Abstract
Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990s. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. Firstly, entanglement is the “quantum teleportation channel”, i.e., entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that Alice, the sender, has to perform jointly on the quantum state to be teleported and her half of the “quantum teleportation channel”, i.e., entanglement enabling entirely new kinds of quantum measurements. I emphasize how poorly this second kind of entanglement is understood. In particular, I use quantum networks in which each party connected to several nodes performs a joint measurement to illustrate that the quantumness of such joint measurements remains elusive, escaping today’s available tools to detect and quantify it.
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Affiliation(s)
- Nicolas Gisin
- Group of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
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48
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Designolle S, Skrzypczyk P, Fröwis F, Brunner N. Quantifying Measurement Incompatibility of Mutually Unbiased Bases. PHYSICAL REVIEW LETTERS 2019; 122:050402. [PMID: 30821992 DOI: 10.1103/physrevlett.122.050402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2018] [Indexed: 06/09/2023]
Abstract
Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness. Specifically, for sets of k MUB in dimension d, we provide upper and lower bounds on this quantity. Notably, we get a tight bound in several cases, in particular for complete sets of k=d+1 MUB (using the standard construction for d being a prime power). On the way, we also derive a general upper bound on the noise robustness for an arbitrary set of quantum measurements. Moreover, we prove the existence of sets of k MUB that are operationally inequivalent, as they feature different noise robustness, and we provide a lower bound on the number of such inequivalent sets up to dimension 32. Finally, we discuss applications of our results for Einstein-Podolsky-Rosen steering.
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Affiliation(s)
- Sébastien Designolle
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Paul Skrzypczyk
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Florian Fröwis
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Nicolas Brunner
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
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49
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Yang Y, Zhang C, Cao H. Approximating Ground States by Neural Network Quantum States. ENTROPY 2019; 21:e21010082. [PMID: 33266798 PMCID: PMC7514192 DOI: 10.3390/e21010082] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/16/2018] [Revised: 01/06/2019] [Accepted: 01/16/2019] [Indexed: 11/16/2022]
Abstract
Motivated by the Carleo’s work (Science, 2017, 355: 602), we focus on finding the neural network quantum statesapproximation of the unknown ground state of a given Hamiltonian H in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.
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Affiliation(s)
- Ying Yang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China
- School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China
| | - Chengyang Zhang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China
| | - Huaixin Cao
- School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China
- Correspondence:
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50
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Cavaillès A, Le Jeannic H, Raskop J, Guccione G, Markham D, Diamanti E, Shaw MD, Verma VB, Nam SW, Laurat J. Demonstration of Einstein-Podolsky-Rosen Steering Using Hybrid Continuous- and Discrete-Variable Entanglement of Light. PHYSICAL REVIEW LETTERS 2018; 121:170403. [PMID: 30411932 DOI: 10.1103/physrevlett.121.170403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2018] [Indexed: 06/08/2023]
Abstract
Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided device-independent quantum information protocols. Here we demonstrate steering using hybrid entanglement between continuous- and discrete-variable optical qubits. To this end, we report on suitable steering inequalities and detail the implementation and requirements for this demonstration. Steering is experimentally certified by observing a violation by more than 5 standard deviations. Our results illustrate the potential of optical hybrid entanglement for applications in heterogeneous quantum networks that would interconnect disparate physical platforms and encodings.
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Affiliation(s)
- A Cavaillès
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - H Le Jeannic
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - J Raskop
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - G Guccione
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - D Markham
- Laboratoire d'Informatique de Paris 6, Sorbonne Université, CNRS, 4 Place Jussieu, 75005 Paris, France
| | - E Diamanti
- Laboratoire d'Informatique de Paris 6, Sorbonne Université, CNRS, 4 Place Jussieu, 75005 Paris, France
| | - M D Shaw
- Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA
| | - V B Verma
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - S W Nam
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - J Laurat
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, 4 Place Jussieu, 75005 Paris, France
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