Contextuality, superlocality and nonclassicality of supernoncontextuality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911361612644352 |
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| author | Jebarathinam, Chellasamy Srikanth, R. |
| author_facet | Jebarathinam, Chellasamy Srikanth, R. |
| contents | Contextuality is a fundamental manifestation of nonclassicality, indicating that for certain quantum correlations, sets of jointly measurable variables cannot be pre-assigned values independently of the measurement context. In this work, we characterize nonclassical quantum correlation beyond contextuality, in terms of supernoncontextuality, namely the higher-than-quantum hidden-variable(HV) dimensionality required to reproduce the given noncontextual quantum correlations. Thus supernoncontextuality is the contextuality analogue of superlocality. Specifically, we study the quantum system of two-qubit states in a scenario composed of five contexts that demonstrate contextuality in a state-dependent fashion. For this purpose, we use the framework of boxes, whose behavior is described by a set of probabilities satisfying the no-disturbance conditions. We first demonstrate that while superlocality is necessary to observe a contextual box, superlocality is not sufficient for contextuality. On the other hand, a noncontextual superlocal box can be supernoncontextual, but superlocality is not a necessary condition. We then introduce a notion of nonclassicality beyond the standard contextuality, called semi-device-independent contextuality. We study semi-device-independent contextuality of two-qubit states in the above mentioned scenario and demonstrate how supernoncontextuality implies this nonclassicality. To this end, we propose a criterion and a measure of semi-device-independent contextuality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contextuality, superlocality and nonclassicality of supernoncontextuality Jebarathinam, Chellasamy Srikanth, R. Quantum Physics Contextuality is a fundamental manifestation of nonclassicality, indicating that for certain quantum correlations, sets of jointly measurable variables cannot be pre-assigned values independently of the measurement context. In this work, we characterize nonclassical quantum correlation beyond contextuality, in terms of supernoncontextuality, namely the higher-than-quantum hidden-variable(HV) dimensionality required to reproduce the given noncontextual quantum correlations. Thus supernoncontextuality is the contextuality analogue of superlocality. Specifically, we study the quantum system of two-qubit states in a scenario composed of five contexts that demonstrate contextuality in a state-dependent fashion. For this purpose, we use the framework of boxes, whose behavior is described by a set of probabilities satisfying the no-disturbance conditions. We first demonstrate that while superlocality is necessary to observe a contextual box, superlocality is not sufficient for contextuality. On the other hand, a noncontextual superlocal box can be supernoncontextual, but superlocality is not a necessary condition. We then introduce a notion of nonclassicality beyond the standard contextuality, called semi-device-independent contextuality. We study semi-device-independent contextuality of two-qubit states in the above mentioned scenario and demonstrate how supernoncontextuality implies this nonclassicality. To this end, we propose a criterion and a measure of semi-device-independent contextuality. |
| title | Contextuality, superlocality and nonclassicality of supernoncontextuality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2403.01762 |