{"paper":{"title":"A geometric Fano--Procrustes framework for purification-based distances and quantum channels analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Trist\\'an M. Os\\'an","submitted_at":"2026-05-18T14:36:56Z","abstract_excerpt":"In this work we reformulate the Uhlmann purification-overlap optimization and develop a purification-based geometric framework for the analysis of mixed qubit states and qubit channels. Using the Fano representation of two-qubit pure states, a purification is described in terms of the Bloch vector of the system, the ancilla Bloch vector, and a real correlation matrix. For a fixed one-qubit mixed state, the freedom in the choice of purification can be parametrized by proper rotations acting on the ancillary degrees of freedom. As a result, the optimization over purifications entering the defini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18485","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/2605.18485/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"}