{"paper":{"title":"Restriction on the rank of marginals of bipartite pure states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"S.V.M. Satyanarayana","submitted_at":"2013-05-16T02:41:29Z","abstract_excerpt":"Consider a qubit-qutrit ($2 \\times 3$) composite state space. Let $C(\\{1}{2}I_2, \\{1}{3}I_3)$ be a convex set of all possible states of composite system whose marginals are given by $\\{1}{2}I_2$ and $\\{1}{3}I_3$ in two and three dimensional spaces respectively. We prove that there exists no pure state in $C(\\{1}{2}I_2, \\{1}{3}I_3)$. Further we generalize this result to an arbitrary $m \\times n$ bipartite systems. We prove that for $m < n$, no pure state exists in the convex set $C(\\rho_A,\\rho_B)$, for an arbitrary $\\rho_A$ and rank of $\\rho_B >m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3672","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"}