{"paper":{"title":"Formulas for Generalized Two-Qubit Separability Probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Paul B. Slater","submitted_at":"2016-09-27T18:15:09Z","abstract_excerpt":"To begin, we find certain formulas $Q(k,\\alpha)= G_1^k(\\alpha) G_2^k(\\alpha)$, for $k = -1, 0, 1,...,9$. These yield that part of the total separability probability, $P(k,\\alpha)$, for generalized (real, complex, quaternionic,\\ldots) two-qubit states endowed with random induced measure, for which the determinantal inequality $|\\rho^{PT}| >|\\rho|$ holds. Here $\\rho$ denotes a $4 \\times 4$ density matrix, obtained by tracing over the pure states in $4 \\times (4 +k)$-dimensions, and $\\rho^{PT}$, its partial transpose. Further, $\\alpha$ is a Dyson-index-like parameter with $\\alpha = 1$ for the sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08561","kind":"arxiv","version":3},"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"}