Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality

• URL: http://arxiv.org/abs/2404.04048v2
• Date: Tue, 9 Apr 2024 14:38:46 GMT
• Title: Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
• Authors: Ruo-Chen Wang, Zhuo-Chen Li, Xing-Yan Fan, Xiang-Ru Xie, Hong-Hao Wei, Choo Hiap Oh, Jing-Ling Chen,
• Abstract summary: The Werner state is a benchmark to test the boundary between quantum mechanics and classical models. In this work, we focus on EPR steering, which is a form of quantum nonlocality intermediate between entanglement and Bell's nonlocality.
• Score: 8.344818267139367
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In quantum information, the Werner state is a benchmark to test the boundary between quantum mechanics and classical models. There have been three well-known critical values for the two-qubit Werner state, i.e., $V_{\rm c}^{\rm E}=1/3$ characterizing the boundary between entanglement and separable model, $V_{\rm c}^{\rm B}=1/K_G(3)$ characterizing the boundary between Bell's nonlocality and the local-hidden-variable model, while $V_{\rm c}^{\rm S}=1/2$ characterizing the boundary between Einstein-Podolsky-Rosen (EPR) steering and the local-hidden-state model. So far, the problem of $V_{\rm c}^{\rm E}=1/3$ has been completely solved by an inequality involving in the positive-partial-transpose criterion, while how to reveal the other two critical values by the inequality approach are still open. In this work, we focus on EPR steering, which is a form of quantum nonlocality intermediate between entanglement and Bell's nonlocality. By proposing the optimal $N$-setting linear EPR-steering inequalities, we have successfully obtained the desired value $V_{\rm c}^{\rm S}=1/2$ for the two-qubit Werner state, thus resolving the long-standing problem.

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