scholarly journals Deriving Einstein–Podolsky–Rosen steering inequalities from the few-body Abner Shimony inequalities

2018 ◽  
Vol 33 (12) ◽  
pp. 1850064
Author(s):  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Shu-Han Jiang ◽  
Zhen-Peng Xu ◽  
Changliang Ren ◽  
...  
Keyword(s):  
Quantum Nonlocality ◽  
Hidden Variable ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
Epr Steering ◽  
Local Hidden Variable

For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein–Podolsky–Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell nonlocality.

scholarly journals Wigner’s Variant of Bell’s Inequality

1998 ◽  
Vol 51 (5) ◽  
pp. 835 ◽  
Author(s):  
Johannes F. Geurdes
Keyword(s):  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Hidden Variable ◽  
Einstein Podolsky Rosen ◽  
Local Hidden Variable

It is shown that Wigner’s variant of Bell’s inequality does not exclude all local hidden variable explanations of the Einstein–Podolsky–Rosen problem.

scholarly journals Exploring Multipartite Steering Effect Using Bell Operators

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 19
Author(s):  
Li-Yi Hsu ◽  
Shoichi Kawamoto
Keyword(s):  
Quantum Correlation ◽  
Numerical Results ◽  
Quantum Network ◽  
Joint Measurability ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
The One ◽  
Necessary And Sufficient ◽  
Qubit States ◽  
Epr Steering

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

scholarly journals Einstein-Podolsky-Rosen Steering Inequalities and Applications

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 683 ◽  
Author(s):  
Ying Yang ◽  
Huaixin Cao
Keyword(s):  
Quantum System ◽  
Quantum Correlation ◽  
Entangled State ◽  
Intermediate Type ◽  
Maximally Entangled State ◽  
Nonlocal Correlation ◽  
Composite Quantum System ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
Epr Steering

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.

scholarly journals The Einstein–Podolsky–Rosen Steering and Its Certification

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 422 ◽  
Author(s):  
Yi-Zheng Zhen ◽  
Xin-Yu Xu ◽  
Li Li ◽  
Nai-Le Liu ◽  
Kai Chen
Keyword(s):  
Local Effects ◽  
Basic Framework ◽  
Quantum Protocols ◽  
Einstein Podolsky Rosen ◽  
Non Local ◽  
Bell Nonlocality ◽  
Epr Steering

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.

scholarly journals Single-copy activation of Bell nonlocality via broadcasting of quantum states

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 499
Author(s):  
Joseph Bowles ◽  
Flavien Hirsch ◽  
Daniel Cavalcanti
Keyword(s):  
Single Copy ◽  
Quantum Correlations ◽  
The State ◽  
Mixed States ◽  
Variable Model ◽  
Variable Theory ◽  
Hidden Variable ◽  
Bell Nonlocality ◽  
Nonlocal Nature ◽  
Local Hidden Variable

Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state:ρα=α|Φ+⟩⟨Φ+|+(1−α)14.We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12, in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.

scholarly journals Quantum postulate vs. quantum nonlocality: on the role of the Planck constant in Bell’s argument

2021 ◽  
Vol 51 (1) ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Nonlocality ◽  
Quantum Mechanical ◽  
Quantum Foundations ◽  
Planck Constant ◽  
Variable Model ◽  
Basic Principles ◽  
Fundamental Feature ◽  
Hidden Variable ◽  
Bell Model

AbstractWe present a quantum mechanical (QM) analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of QM, Bell’s model implies rejection of this postulate as well. Thus, this hidden-variable model contradicts not only the QM-formalism, but also the fundamental feature of the quantum world discovered by Planck.

scholarly journals Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 185 ◽  
Author(s):  
Yeong-Cherng Liang ◽  
Yanbao Zhang
Keyword(s):  
Hypothesis Testing ◽  
Hypothesis Test ◽  
Quantum Correlations ◽  
Ratio Method ◽  
Empirical Observation ◽  
Hidden Variable ◽  
Apparent Violation ◽  
Hidden Variable Theories ◽  
Experimental Trials ◽  
Local Hidden Variable

The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell’s seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method—initially developed for performing a hypothesis test of local-hidden-variable theories—can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.

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