{"paper":{"title":"The Quantum Correction to Gaussian Information Geometry is the Killing Form of the Symplectic Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Christian Kerskens","submitted_at":"2026-07-17T15:35:42Z","abstract_excerpt":"On the admissible cone $\\mathcal C_\\Omega=\\{\\Sigma\\in\\mathrm{Sym}^+(2n):\\Sigma+i\\Omega\\ge0\\}$ of Gaussian covariance matrices, the classical Bures--Wasserstein transport metric, the Fisher--Rao information metric, and the quantum Bures metric are individually well understood, but their mutual relationship is obscured by the operator equations defining them. Working with the contravariant (dual) metrics, we show that the exact difference between the dual quantum Bures metric and the dual Fisher--Rao metric is independent of the covariance matrix: it is identically the trace form, proportional t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16376/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}