Lower-bounding entanglement with nonlocality in a general Bell's scenario
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913043099680768 |
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| author | Sun, Liang-Liang Zhou, Xiang Xu, Zhen-Peng Yu, Sixia |
| author_facet | Sun, Liang-Liang Zhou, Xiang Xu, Zhen-Peng Yu, Sixia |
| contents | Understanding the quantitative relation between entanglement and Bell nonlocality is a long-standing open problem of fundamental and practical interest. Here, we tackle this problem in a general Bell scenario. {We observe that lying in the center of quantifying these properties are two minimal distances: one from a state to separable states (entanglement), and the other from a correlation to local correlations (nonlocality).} We find that these two distances can be related to each other -- the minimal correlation distance provides a lower bound for the minimal state distance, which allows us to derive nontrivial bounds on many entanglement measures with an arbitrary nonlocal correlation. Moreover, with the on-hand structural knowledge of entanglement and nonlocality in the $(n, 2, 2)$ Bell scenario, we refine our estimate significantly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02588 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lower-bounding entanglement with nonlocality in a general Bell's scenario Sun, Liang-Liang Zhou, Xiang Xu, Zhen-Peng Yu, Sixia Quantum Physics Understanding the quantitative relation between entanglement and Bell nonlocality is a long-standing open problem of fundamental and practical interest. Here, we tackle this problem in a general Bell scenario. {We observe that lying in the center of quantifying these properties are two minimal distances: one from a state to separable states (entanglement), and the other from a correlation to local correlations (nonlocality).} We find that these two distances can be related to each other -- the minimal correlation distance provides a lower bound for the minimal state distance, which allows us to derive nontrivial bounds on many entanglement measures with an arbitrary nonlocal correlation. Moreover, with the on-hand structural knowledge of entanglement and nonlocality in the $(n, 2, 2)$ Bell scenario, we refine our estimate significantly. |
| title | Lower-bounding entanglement with nonlocality in a general Bell's scenario |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2312.02588 |