51
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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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52
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Yang Y, Cao H. Einstein-Podolsky-Rosen Steering Inequalities and Applications. ENTROPY 2018; 20:e20090683. [PMID: 33265772 PMCID: PMC7513208 DOI: 10.3390/e20090683] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Revised: 09/01/2018] [Accepted: 09/05/2018] [Indexed: 11/25/2022]
Abstract
Einstein-Podolsky-Rosen (EPR) steering is very important quantum correlation of a composite quantum system. It is an intermediate type of nonlocal correlation between entanglement and Bell nonlocality. In this paper, based on introducing definitions and characterizations of EPR steering, some EPR steering inequalities are derived. With these inequalities, the steerability of the maximally entangled state is checked and some conditions for the steerability of the X-states are obtained.
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Affiliation(s)
- Ying Yang
- School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
- School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China
| | - Huaixin Cao
- School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
- Correspondence:
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53
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Skrzypczyk P, Cavalcanti D. Maximal Randomness Generation from Steering Inequality Violations Using Qudits. PHYSICAL REVIEW LETTERS 2018; 120:260401. [PMID: 30004726 DOI: 10.1103/physrevlett.120.260401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Revised: 05/16/2018] [Indexed: 06/08/2023]
Abstract
We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.
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Affiliation(s)
- Paul Skrzypczyk
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - Daniel Cavalcanti
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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54
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Toscano F, Tasca DS, Rudnicki Ł, Walborn SP. Uncertainty Relations for Coarse-Grained Measurements: An Overview. ENTROPY (BASEL, SWITZERLAND) 2018; 20:E454. [PMID: 33265544 PMCID: PMC7512973 DOI: 10.3390/e20060454] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 06/02/2018] [Accepted: 06/06/2018] [Indexed: 12/04/2022]
Abstract
Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.
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Affiliation(s)
- Fabricio Toscano
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Brazil
| | - Daniel S. Tasca
- Instituto de Física, Universidade Federal Fluminense, Niteroi 24210-346, Brazil
| | - Łukasz Rudnicki
- Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, Erlangen 91058, Germany
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, Warsaw 02-668, Poland
| | - Stephen P. Walborn
- Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Brazil
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Abstract
Entanglement survives between spatially separated atoms of an atomic cloud after it expands
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Affiliation(s)
- Daniel Cavalcanti
- Institut de Ciències Fotòniques (ICFO), The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.
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56
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Fadel M, Zibold T, Décamps B, Treutlein P. Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates. Science 2018; 360:409-413. [DOI: 10.1126/science.aao1850] [Citation(s) in RCA: 139] [Impact Index Per Article: 23.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 03/13/2018] [Indexed: 11/03/2022]
Abstract
Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.
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Affiliation(s)
- Matteo Fadel
- Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Tilman Zibold
- Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Boris Décamps
- Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Philipp Treutlein
- Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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57
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Kunkel P, Prüfer M, Strobel H, Linnemann D, Frölian A, Gasenzer T, Gärttner M, Oberthaler MK. Spatially distributed multipartite entanglement enables EPR steering of atomic clouds. Science 2018; 360:413-416. [DOI: 10.1126/science.aao2254] [Citation(s) in RCA: 125] [Impact Index Per Article: 20.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 02/16/2018] [Indexed: 11/02/2022]
Abstract
A key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. However, the robust generation and detection of entanglement between spatially separated regions of an ultracold atomic system remain a challenge. We used spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this entanglement can be spatially distributed by self-similar expansion of the atomic cloud. We used spatially resolved spin read-out to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Based on the strength of EPR steering, we constructed a witness, which confirmed genuine 5-partite entanglement.
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Affiliation(s)
- Philipp Kunkel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Maximilian Prüfer
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Daniel Linnemann
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Anika Frölian
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Martin Gärttner
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K. Oberthaler
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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58
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Nery RV, Taddei MM, Chaves R, Aolita L. Quantum Steering Beyond Instrumental Causal Networks. PHYSICAL REVIEW LETTERS 2018; 120:140408. [PMID: 29694116 DOI: 10.1103/physrevlett.120.140408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2017] [Indexed: 06/08/2023]
Abstract
We theoretically predict, and experimentally verify with entangled photons, that outcome communication is not enough for hidden-state models to reproduce quantum steering. Hidden-state models with outcome communication correspond, in turn, to the well-known instrumental processes of causal inference but in the one-sided device-independent scenario of one black-box measurement device and one well-characterized quantum apparatus. We introduce one-sided device-independent instrumental inequalities to test against these models, with the appealing feature of detecting entanglement even when communication of the black box's measurement outcome is allowed. We find that, remarkably, these inequalities can also be violated solely with steering, i.e., without outcome communication. In fact, an efficiently computable formal quantifier-the robustness of noninstrumentality-naturally arises, and we prove that steering alone is enough to maximize it. Our findings imply that quantum theory admits a stronger form of steering than known until now, with fundamental as well as practical potential implications.
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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
| | - R Chaves
- International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613, Natal, 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
- ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, UNESP-Universidade Estadual Paulista R. Dr. Bento T. Ferraz 271, Bl. II, São Paulo, São Paulo 01140-070, Brazil
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59
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Wang J, Paesani S, Ding Y, Santagati R, Skrzypczyk P, Salavrakos A, Tura J, Augusiak R, Mančinska L, Bacco D, Bonneau D, Silverstone JW, Gong Q, Acín A, Rottwitt K, Oxenløwe LK, O’Brien JL, Laing A, Thompson MG. Multidimensional quantum entanglement with large-scale integrated optics. Science 2018. [DOI: 10.1126/science.aar7053] [Citation(s) in RCA: 398] [Impact Index Per Article: 66.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
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60
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Abstract
Occupying a position between entanglement and Bell nonlocality, Einstein-Podolsky-Rosen (EPR) steering has attracted increasing attention in recent years. Many criteria have been proposed and experimentally implemented to characterize EPR-steering. Nevertheless, only a few results are available to quantify steerability using analytical results. In this work, we propose a method for quantifying the steerability in two-qubit quantum states in the two-setting EPR-steering scenario, using the connection between joint measurability and steerability. We derive an analytical formula for the steerability of a class of X-states. The sufficient and necessary conditions for two-setting EPR-steering are presented. Based on these results, a class of asymmetric states, namely, one-way steerable states, are obtained.
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Abstract
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of the natural world, from understanding counter-intuitive concepts to the development of wholly quantum-mechanical technology. Here, we show that quantum-mechanical processes can be quantified using a generic classical-process model through which any classical strategies of mimicry can be ruled out. We demonstrate the success of this formalism using fundamental processes postulated in quantum mechanics, the dynamics of open quantum systems, quantum-information processing, the fusion of entangled photon pairs, and the energy transfer in a photosynthetic pigment-protein complex. Since our framework does not depend on any specifics of the states being processed, it reveals a new class of correlations in the hierarchy between entanglement and Einstein-Podolsky-Rosen steering and paves the way for the elaboration of a generic method for quantifying physical processes.
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62
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Cavalcanti D, Skrzypczyk P, Šupić I. All Entangled States can Demonstrate Nonclassical Teleportation. PHYSICAL REVIEW LETTERS 2017; 119:110501. [PMID: 28949233 DOI: 10.1103/physrevlett.119.110501] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2017] [Indexed: 06/07/2023]
Abstract
Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using preshared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and prove that all entangled states can implement a quantum channel which cannot be reproduced classically. We introduce the idea of nonclassical teleportation witness to certify if a teleportation experiment is genuinely quantum and discuss how to quantify this phenomenon. Our work provides new techniques for studying teleportation that can be immediately applied to certify the quality of quantum technologies.
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Affiliation(s)
- Daniel Cavalcanti
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Paul Skrzypczyk
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Ivan Šupić
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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