A linear program for testing nonclassicality and an open-source implementation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913297914134528 |
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| author | Selby, John H. Wolfe, Elie Schmid, David Sainz, Ana Belén Rossi, Vinicius P. |
| author_facet | Selby, John H. Wolfe, Elie Schmid, David Sainz, Ana Belén Rossi, Vinicius P. |
| contents | A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex-embeddability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11905 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A linear program for testing nonclassicality and an open-source implementation Selby, John H. Wolfe, Elie Schmid, David Sainz, Ana Belén Rossi, Vinicius P. Quantum Physics A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an arbitrary set of quantum states and an arbitrary set of quantum effects; the program then determines if the Born rule statistics generated by all pairs of these can be explained by a classical (noncontextual) model. If a classical model exists, it provides an explicit model. If it does not, then it computes the minimal amount of noise that must be added such that a model does exist, and then provides this model. We generalize all these results to arbitrary generalized probabilistic theories (and accessible fragments thereof) as well; indeed, our linear program is a test of simplex-embeddability. |
| title | A linear program for testing nonclassicality and an open-source implementation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2204.11905 |