{"paper":{"title":"Volumes of conditioned bipartite state spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Simon Milz, Walter T. Strunz","submitted_at":"2014-08-15T22:10:14Z","abstract_excerpt":"We analyse the metric properties of $\\textit{conditioned}$ quantum state spaces $\\mathcal{M}^{(n\\times m)}_{\\eta}$. These spaces are the convex sets of $nm \\times nm$ density matrices that, when partially traced over $m$ degrees of freedom, respectively yield the given $n\\times n$ density matrix $\\eta$. For the case $n=2$, the volume of $\\mathcal{M}^{(2\\times m)}_{\\eta}$ equipped with the Hilbert-Schmidt measure is a simple polynomial of the radius of $\\eta$ in the Bloch-Ball. Remarkably, the probability $p_{\\mathrm{sep}}^{(2\\times m)}(\\eta)$ to find a separable state in $\\mathcal{M}^{(2\\times"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3666","kind":"arxiv","version":2},"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"}