Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917451488296960 |
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| author | Hazra, Soumyabrata Saha, Debashis Chaturvedi, Anubhav Bera, Subhankar Majumdar, A. S. |
| author_facet | Hazra, Soumyabrata Saha, Debashis Chaturvedi, Anubhav Bera, Subhankar Majumdar, A. S. |
| contents | Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the noncontextual polytope while ensuring that the dimension of the polytope associated with the preparations remains constant regardless of the number of measurements and their outcome size. The facet inequalities of the noncontextual polytope can thus be obtained in a computationally efficient manner. We illustrate the efficacy of our methodology through several distinct contextuality scenarios. Our investigation uncovers several hitherto unexplored noncontextuality inequalities and demonstrates applications of quantum contextual correlations in certification of non-projective measurements, witnessing the dimension of quantum systems, and randomness certification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities Hazra, Soumyabrata Saha, Debashis Chaturvedi, Anubhav Bera, Subhankar Majumdar, A. S. Quantum Physics Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the noncontextual polytope while ensuring that the dimension of the polytope associated with the preparations remains constant regardless of the number of measurements and their outcome size. The facet inequalities of the noncontextual polytope can thus be obtained in a computationally efficient manner. We illustrate the efficacy of our methodology through several distinct contextuality scenarios. Our investigation uncovers several hitherto unexplored noncontextuality inequalities and demonstrates applications of quantum contextual correlations in certification of non-projective measurements, witnessing the dimension of quantum systems, and randomness certification. |
| title | Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.09111 |