dorsal/arxiv
View SchemaBell Inequalities in Phase Space and their Violation in Quantum Mechanics
| Authors | G. Auberson, G. Mahoux, S. M. Roy, Virendra Singh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205157 |
| URL | https://arxiv.org/abs/quant-ph/0205157 |
| DOI | 10.1016/S0375-9601(02)00827-7 |
Abstract
We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there exist quantum states for which more than three of the quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and $(p_1,q_2)$ cannot be reproduced as marginals of a positive $\rho(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most general positive $\rho(\overrightarrow{q},\overrightarrow{p})$ which reproduces any three of the above quantum probability densities for arbitrary quantum states. This is crucial for the construction of a maximally realistic quantum theory.
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"abstract": "We derive ``Bell inequalities\u0027\u0027 in four dimensional phase space and prove the\nfollowing ``three marginal theorem\u0027\u0027 for phase space densities\n$\\rho(\\overrightarrow{q},\\overrightarrow{p})$, thus settling a long standing\nconjecture : ``there exist quantum states for which more than three of the\nquantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and\n$(p_1,q_2)$ cannot be reproduced as marginals of a positive\n$\\rho(\\overrightarrow{q},\\overrightarrow{p})$\u0027\u0027. We also construct the most\ngeneral positive $\\rho(\\overrightarrow{q},\\overrightarrow{p})$ which reproduces\nany three of the above quantum probability densities for arbitrary quantum\nstates. This is crucial for the construction of a maximally realistic quantum\ntheory.",
"arxiv_id": "quant-ph/0205157",
"authors": [
"G. Auberson",
"G. Mahoux",
"S. M. Roy",
"Virendra Singh"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(02)00827-7",
"title": "Bell Inequalities in Phase Space and their Violation in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0205157"
},
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