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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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2
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Jabbour MG, Brask JB. Constructing Local Models for General Measurements on Bosonic Gaussian States. PHYSICAL REVIEW LETTERS 2023; 131:110202. [PMID: 37774297 DOI: 10.1103/physrevlett.131.110202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Revised: 05/23/2023] [Accepted: 08/22/2023] [Indexed: 10/01/2023]
Abstract
We derive a simple sufficient criterion for the locality of correlations obtained from given measurements on a Gaussian quantum state. The criterion is based on the construction of a local-hidden-variable model that works by passing part of the inherent Gaussian noise of the state onto the measurements. We illustrate our result in the setting of displaced photodetection on a two-mode squeezed state. Here, our criterion exhibits the existence of a local-hidden-variable model for a range of parameters where the state is still entangled.
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Affiliation(s)
- Michael G Jabbour
- Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
| | - Jonatan Bohr Brask
- Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark
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3
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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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4
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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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5
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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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6
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Bowles J, Šupić I, Cavalcanti D, Acín A. Device-Independent Entanglement Certification of All Entangled States. PHYSICAL REVIEW LETTERS 2018; 121:180503. [PMID: 30444410 DOI: 10.1103/physrevlett.121.180503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2018] [Indexed: 06/09/2023]
Abstract
We present a method to certify the entanglement of all entangled quantum states in a device-independent way. This is achieved by placing the state in a quantum network and constructing a correlation inequality based on an entanglement witness for the state. Our method is device independent, in the sense that entanglement can be certified from the observed statistics alone, under minimal assumptions on the underlying physics. Conceptually, our results borrow ideas from the field of self-testing to bring the recently introduced measurement-device-independent entanglement witnesses into the fully device-independent regime.
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Affiliation(s)
- Joseph Bowles
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Ivan Šupić
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Daniel Cavalcanti
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Antonio Acín
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Pg. Lluis Companys 23, Barcelona 08010, Spain
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7
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Costa ACS, Uola R, Gühne O. Entropic Steering Criteria: Applications to Bipartite and Tripartite Systems. ENTROPY 2018; 20:e20100763. [PMID: 33265852 PMCID: PMC7512325 DOI: 10.3390/e20100763] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2018] [Revised: 09/19/2018] [Accepted: 09/20/2018] [Indexed: 11/16/2022]
Abstract
The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and Rényi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.
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8
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Tóth G, Vértesi T. Quantum States with a Positive Partial Transpose are Useful for Metrology. PHYSICAL REVIEW LETTERS 2018; 120:020506. [PMID: 29376687 DOI: 10.1103/physrevlett.120.020506] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2017] [Indexed: 06/07/2023]
Abstract
We show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find such states. We present some examples for multipartite states and examine the scaling of the precision with the particle number. Some bipartite examples are also shown that possess an entanglement very robust to noise. We also discuss the relation of metrological usefulness to Bell inequality violation. We find that quantum states that do not violate any Bell inequality can outperform separable states metrologically. We present such states with a positive partial transpose, as well as with a nonpositive partial transpose.
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Affiliation(s)
- Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
- Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Tamás Vértesi
- Institute for Nuclear Research, Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary
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Miller CA, Colbeck R, Shi Y. Keyring models: an approach to steerability. JOURNAL OF MATHEMATICAL PHYSICS 2018; 59:10.1063/1.5006199. [PMID: 30983628 PMCID: PMC6459415 DOI: 10.1063/1.5006199] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
If a measurement is made on one half of a bipartite system, then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation-that is, if shared randomness cannot produce these reduced states for all possible measurements-the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models-a special class of local hidden state models. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels.
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Affiliation(s)
- Carl A. Miller
- National Institute of Standards and Technology 100 Bureau Dr., Gaithersburg, MD 20899, USA
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - Roger Colbeck
- Department of Mathematics, University of York, York, YO10 5DD, UK
| | - Yaoyun Shi
- Aliyun Quantum Laboratory, Alibaba USA, Bellevue, WA 98004, USA
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10
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Oszmaniec M, Guerini L, Wittek P, Acín A. Simulating Positive-Operator-Valued Measures with Projective Measurements. PHYSICAL REVIEW LETTERS 2017; 119:190501. [PMID: 29219480 DOI: 10.1103/physrevlett.119.190501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Indexed: 06/07/2023]
Abstract
Standard projective measurements (PMs) represent a subset of all possible measurements in quantum physics, defined by positive-operator-valued measures. We study what quantum measurements are projective simulable, that is, can be simulated by using projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realized by classical randomization of projective measurements on the system plus an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is PM simulable can be solved by means of semidefinite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our work provides bounds on the amount of white noise a measurement tolerates before losing any advantage over projective ones.
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Affiliation(s)
- Michał Oszmaniec
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland
- Faculty of Mathematics, Physics and Informatics, Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
| | - Leonardo Guerini
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Departamento de Matemática, Universidade Federal de Minas Gerais, Caixa Postal 702, 31270-901, Belo Horizonte, MG, Brazil
| | - Peter Wittek
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- University of Borås, 50190 Borås, Sweden
| | - Antonio Acín
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain
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Cavalcanti D, Skrzypczyk P. Quantum steering: a review with focus on semidefinite programming. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:024001. [PMID: 28008876 DOI: 10.1088/1361-6633/80/2/024001] [Citation(s) in RCA: 60] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Quantum steering refers to the non-classical correlations that can be observed between the outcomes of measurements applied on half of an entangled state and the resulting post-measured states that are left with the other party. From an operational point of view, a steering test can be seen as an entanglement test where one of the parties performs uncharacterised measurements. Thus, quantum steering is a form of quantum inseparability that lies in between the well-known notions of Bell nonlocality and entanglement. Moreover, quantum steering is also related to several asymmetric quantum information protocols where some of the parties are considered untrusted. Because of these facts, quantum steering has received a lot of attention both theoretically and experimentally. The main goal of this review is to give an overview of how to characterise quantum steering through semidefinite programming. This characterisation provides efficient numerical methods to address a number of problems, including steering detection, quantification, and applications. We also give a brief overview of some important results that are not directly related to semidefinite programming. Finally, we make available a collection of semidefinite programming codes that can be used to study the topics discussed in this article.
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Affiliation(s)
- D Cavalcanti
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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12
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Hirsch F, Quintino MT, Vértesi T, Pusey MF, Brunner N. Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States. PHYSICAL REVIEW LETTERS 2016; 117:190402. [PMID: 27858440 DOI: 10.1103/physrevlett.117.190402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2015] [Indexed: 06/06/2023]
Abstract
Constructing local hidden variable (LHV) models for entangled quantum states is a fundamental problem, with implications for the foundations of quantum theory and for quantum information processing. It is, however, a challenging problem, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models, applicable to any entangled state and considering continuous sets of measurements. This leads to a sequence of tests which, in the limit, fully captures the set of quantum states admitting a LHV model. Similar methods are developed for local hidden state models. We illustrate the practical relevance of these methods with several examples.
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Affiliation(s)
- Flavien Hirsch
- Département de Physique Théorique, Université de Genéve, 1211 Genéve, Switzerland
| | - Marco Túlio Quintino
- Département de Physique Théorique, Université de Genéve, 1211 Genéve, Switzerland
| | - Tamás Vértesi
- Institute for Nuclear Research, Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary
| | - Matthew F Pusey
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada
| | - Nicolas Brunner
- Département de Physique Théorique, Université de Genéve, 1211 Genéve, Switzerland
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13
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Nagy S, Vértesi T. EPR Steering inequalities with Communication Assistance. Sci Rep 2016; 6:21634. [PMID: 26880376 PMCID: PMC4754951 DOI: 10.1038/srep21634] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2015] [Accepted: 01/20/2016] [Indexed: 11/19/2022] Open
Abstract
In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with c bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information (c = 1), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.
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Affiliation(s)
- Sándor Nagy
- Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, P.O. Box 5, Hungary
| | - Tamás Vértesi
- Institute for Nuclear Research, Hungarian Academy of Sciences, H-4001 Debrecen, P.O. Box 51, Hungary
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