The Einstein–Podolsky–Rosen Steering and Its Certification

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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Exploring Multipartite Steering Effect Using Bell Operators

Entropy ◽

10.3390/e22010019 ◽

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.

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Einstein-Podolsky-Rosen Steering Inequalities and Applications

Entropy ◽

10.3390/e20090683 ◽

2018 ◽

Vol 20 (9) ◽

pp. 683 ◽

Cited By ~ 3

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.

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

Modern Physics Letters A ◽

10.1142/s0217732318500645 ◽

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.

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