Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
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2024
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| author | Wang, Ruo-Chen Li, Zhuo-Chen Fan, Xing-Yan Xie, Xiang-Ru Wei, Hong-Hao Oh, Choo Hiap Chen, Jing-Ling |
| author_facet | Wang, Ruo-Chen Li, Zhuo-Chen Fan, Xing-Yan Xie, Xiang-Ru Wei, Hong-Hao Oh, Choo Hiap Chen, Jing-Ling |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality Wang, Ruo-Chen Li, Zhuo-Chen Fan, Xing-Yan Xie, Xiang-Ru Wei, Hong-Hao Oh, Choo Hiap Chen, Jing-Ling Quantum Physics 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. |
| title | Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.04048 |