On random classical marginal problems with applications to quantum information theory
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914459470004224 |
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| author | Jha, Ankit Kumar Nechita, Ion |
| author_facet | Jha, Ankit Kumar Nechita, Ion |
| contents | In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions having the incident vertex distributions as marginals. We provide estimates on the probability that a joint distribution on the graph exists, having the bivariate edge distributions as marginals. Our study is motivated by Fine's theorem in quantum mechanics. We study in great detail the graphs corresponding to CHSH and Bell-Wigner scenarios providing rations of volumes between the local and non-signaling polytopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14153 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On random classical marginal problems with applications to quantum information theory Jha, Ankit Kumar Nechita, Ion Quantum Physics Mathematical Physics Probability In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions having the incident vertex distributions as marginals. We provide estimates on the probability that a joint distribution on the graph exists, having the bivariate edge distributions as marginals. Our study is motivated by Fine's theorem in quantum mechanics. We study in great detail the graphs corresponding to CHSH and Bell-Wigner scenarios providing rations of volumes between the local and non-signaling polytopes. |
| title | On random classical marginal problems with applications to quantum information theory |
| topic | Quantum Physics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2406.14153 |