{"paper":{"title":"The Unique Pure Gaussian State Determined by the Partial Saturation of the Uncertainty Relations of a Mixed Gaussian State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SG","quant-ph"],"primary_cat":"math-ph","authors_text":"Maurice A. de Gosson","submitted_at":"2012-05-23T17:09:37Z","abstract_excerpt":"Let {\\rho} the density matrix of a mixed Gaussian state. Assuming that one of the Robertson--Schr\\\"odinger uncertainty inequalities is saturated by {\\rho}, e.g. ({\\Delta}^{{\\rho}}X_1)^2({\\Delta}^{{\\rho}}P_1)^2={\\Delta}^{{\\rho}}(X_1,P_1)^2+(1/4)\\hbar^2, we show that there exists a unique pure Gaussian state whose Wigner distribution is dominated by that of {\\rho} and having the same variances and covariance {\\Delta}^{{\\rho}}X_1,{\\Delta}^{{\\rho}}P_1, and {\\Delta}^{{\\rho}}(X_1,P_1) as {\\rho}. This property can be viewed as an analytic version of Gromov's non-squeezing theorem in the linear case, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5222","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"}