Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909163744919552 |
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| author | Chen, Kai-Siang Mal, Shiladitya Tabia, Gelo Noel M. Liang, Yeong-Cherng |
| author_facet | Chen, Kai-Siang Mal, Shiladitya Tabia, Gelo Noel M. Liang, Yeong-Cherng |
| contents | As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local-hidden variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A. 98, 062103 (2018)] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, a special case of which is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02045 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario Chen, Kai-Siang Mal, Shiladitya Tabia, Gelo Noel M. Liang, Yeong-Cherng Quantum Physics As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local-hidden variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A. 98, 062103 (2018)] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, a special case of which is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided. |
| title | Hardy-type paradoxes for an arbitrary symmetric bipartite Bell scenario |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2311.02045 |