{"paper":{"title":"A Weighted Spectral Quantum Fidelity","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.FA","authors_text":"Cong Trinh Le, Minh Toan Ho, The Khoi Vu, Trung Hoa Dinh","submitted_at":"2026-05-16T21:37:29Z","abstract_excerpt":"We introduce and study a one-parameter family of fidelity-type quantities based on the weighted spectral geometric mean, which we call the \\emph{weighted spectral fidelity} \\( \\mathsf{F}_t^{\\mathrm{spec}}(\\rho,\\sigma):=\\Tr\\!\\big[\\rho(\\rho^{-1}\\sharp\\sigma)^{2t}\\big],\\ t\\in[0,1]. \\) This family interpolates smoothly between the trivial overlap ($t=0,1$) and the Uhlmann (root) fidelity at $t=\\tfrac12$, and it is distinct from the sandwiched R\\'enyi family except at this midpoint. We establish core structural features-unitary invariance, tensor stabilization and multiplicativity, flip symmetry, e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17167","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/2605.17167/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.755207Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.982004Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c461cad8b3d3138feb1338b98228277675aa9003556acaa65711cfb9362ba920"},"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"}