{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PTLT34GFOWCAQSNHUFI7BSJASQ","short_pith_number":"pith:PTLT34GF","schema_version":"1.0","canonical_sha256":"7cd73df0c575840849a7a151f0c920943e5e368c5626cce2ca638348c2946124","source":{"kind":"arxiv","id":"1205.5222","version":1},"attestation_state":"computed","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, "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.5222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-23T17:09:37Z","cross_cats_sorted":["math.MP","math.SG","quant-ph"],"title_canon_sha256":"102689013ca6b1180d9a1e5f8607a1ee734373960996cd7ca3a6fe15d740e7d1","abstract_canon_sha256":"07b0f8975d258567ff70146ff4c9a4f9658713bba57bb183b16c068142d9203c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:01.980423Z","signature_b64":"jrLbsqm0vVpak925On7OQy2XufJLNIaOuXbAA3EQ8iX5WqYG4ShlH5Vwyob2FWLUAOAAb6gXAaT6ehjv2v/dDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cd73df0c575840849a7a151f0c920943e5e368c5626cce2ca638348c2946124","last_reissued_at":"2026-05-18T03:55:01.979793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:01.979793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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}. 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