Self-testing of Nonmaximal Genuine Entangled States using Tripartite Hardy Relations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908340160823296 |
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| author | Adhikary, Ranendu Sasmal, Souradeep Roy, Arup |
| author_facet | Adhikary, Ranendu Sasmal, Souradeep Roy, Arup |
| contents | We demonstrate that, in the tripartite scenario with all parties' local events being space-like separated, Hardy-type nonlocality constitutes a stronger manifestation of nonlocal correlations than those captured by Mermin-type inequalities, an important distinction that has hitherto remained unrecognised. To substantiate this assertion, we develop a general framework for the characterisation of tripartite correlations by extending the notion of Settings Independence and Outcome Independence beyond their bipartite formulation. This framework highlights the pivotal role of Hardy-type reasoning in the detection and certification of genuine multipartite nonlocality. Furthermore, we show that the tripartite Hardy-nonlocality enables the self-testing of a broad class of pure nonmaximally genuine entangled tripartite states. A key advantage of Hardy-based self-testing over methods based on tripartite Bell inequalities is its ability to certify quantum correlations even in the presence of nonmaximal violations. This, in turn, facilitates the device-independent certification of randomness from Hardy-type correlations. Unlike Bell functionals, which typically enable self-testing of only a single extremal point per inequality, Hardy relation self-tests a set of extremal quantum correlations for any nonzero Hardy probability. We find that the maximum certifiable randomness using Hardy-type correlations is $\log_2 7\approx 2.8073$-bits, highlighting both the practical and foundational significance of Hardy-based techniques for quantum randomness generation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-testing of Nonmaximal Genuine Entangled States using Tripartite Hardy Relations Adhikary, Ranendu Sasmal, Souradeep Roy, Arup Quantum Physics We demonstrate that, in the tripartite scenario with all parties' local events being space-like separated, Hardy-type nonlocality constitutes a stronger manifestation of nonlocal correlations than those captured by Mermin-type inequalities, an important distinction that has hitherto remained unrecognised. To substantiate this assertion, we develop a general framework for the characterisation of tripartite correlations by extending the notion of Settings Independence and Outcome Independence beyond their bipartite formulation. This framework highlights the pivotal role of Hardy-type reasoning in the detection and certification of genuine multipartite nonlocality. Furthermore, we show that the tripartite Hardy-nonlocality enables the self-testing of a broad class of pure nonmaximally genuine entangled tripartite states. A key advantage of Hardy-based self-testing over methods based on tripartite Bell inequalities is its ability to certify quantum correlations even in the presence of nonmaximal violations. This, in turn, facilitates the device-independent certification of randomness from Hardy-type correlations. Unlike Bell functionals, which typically enable self-testing of only a single extremal point per inequality, Hardy relation self-tests a set of extremal quantum correlations for any nonzero Hardy probability. We find that the maximum certifiable randomness using Hardy-type correlations is $\log_2 7\approx 2.8073$-bits, highlighting both the practical and foundational significance of Hardy-based techniques for quantum randomness generation. |
| title | Self-testing of Nonmaximal Genuine Entangled States using Tripartite Hardy Relations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.19491 |