{"paper":{"title":"Convexity of quantum $\\chi^2$-divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank Hansen","submitted_at":"2011-02-15T08:21:10Z","abstract_excerpt":"The quantum \\chi^2-divergence has recently been introduced and applied to quantum channels (quantum Markov processes). In contrast to the classical setting the quantum \\chi^2-divergence is not unique but depends on the choice of quantum statistics. In the reference [11] a special one-parameter family of quantum \\chi^2_\\alpha(\\rho,\\sigma)-divergences for density matrices were studied, and it was established that they are convex functions in (\\rho,\\sigma) for parameter values \\alpha\\in [0,1], thus mirroring the classical theorem for the \\chi^2(p,q)-divergence for probability distributions (p,q)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2989","kind":"arxiv","version":2},"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"}