Maximal Clauser-Horne-Shimony-Holt violation for qubit-qudit states
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917028356423680 |
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| author | Bernal, Alexander Casas, J. Alberto Moreno, Jesus M. |
| author_facet | Bernal, Alexander Casas, J. Alberto Moreno, Jesus M. |
| contents | We evaluate the maximal Clauser-Horne-Shimony-Holt (CHSH) violation for a generic (typically mixed) qubit-qudit state, obtaining easily computable expressions in arbitrary qudit dimension. This represents the optimal (2-2-2) Bell nonlocality for this kind of systems. The work generalizes the well-known Horodeckis result for a qubit-qubit setup. We also give simple lower and upper bounds on that violation. We apply our general results to address a number of issues, namely, we obtain a bound on the degree of purity required in a system to exhibit nonlocality and study the statistics of nonlocality in random density matrices. In addition, we show the impossibility of improving the amount of CHSH violation by embedding the qudit in a Hilbert space of larger dimension. Finally, the general result is illustrated with a family of density matrices in the context of a qubit-qutrit system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal Clauser-Horne-Shimony-Holt violation for qubit-qudit states Bernal, Alexander Casas, J. Alberto Moreno, Jesus M. Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory We evaluate the maximal Clauser-Horne-Shimony-Holt (CHSH) violation for a generic (typically mixed) qubit-qudit state, obtaining easily computable expressions in arbitrary qudit dimension. This represents the optimal (2-2-2) Bell nonlocality for this kind of systems. The work generalizes the well-known Horodeckis result for a qubit-qubit setup. We also give simple lower and upper bounds on that violation. We apply our general results to address a number of issues, namely, we obtain a bound on the degree of purity required in a system to exhibit nonlocality and study the statistics of nonlocality in random density matrices. In addition, we show the impossibility of improving the amount of CHSH violation by embedding the qudit in a Hilbert space of larger dimension. Finally, the general result is illustrated with a family of density matrices in the context of a qubit-qutrit system. |
| title | Maximal Clauser-Horne-Shimony-Holt violation for qubit-qudit states |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.02092 |