{"paper":{"title":"Bell Inequalities in Phase Space and their Violation in Quantum Mechanics","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"G. Auberson (Universit\\'e Montpellier II), G. Mahoux (Centre d'\\'Etudes Nucl\\'eaires de Saclay), Mumbai), S.M. Roy, Virendra Singh (Tata Institute of Fundamental Research","submitted_at":"2002-05-24T17:24:22Z","abstract_excerpt":"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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0205157","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}