{"paper":{"title":"A Game Theoretic Approach to Quantum Information","license":"","headline":"","cross_cats":["cs.GT","cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"V. P. Belavkin, Xianhua Dai","submitted_at":"2007-10-02T15:17:37Z","abstract_excerpt":"This work is an application of game theory to quantum information. In a state estimate, we are given observations distributed according to an unknown distribution $P_{\\theta}$ (associated with award $Q$), which Nature chooses at random from the set $\\{P_{\\theta}: \\theta \\in \\Theta \\}$ according to a known prior distribution $\\mu$ on $\\Theta$, we produce an estimate $M$ for the unknown distribution $P_{\\theta}$, and in the end, we will suffer a relative entropy cost $\\mathcal{R}(P;M)$, measuring the quality of this estimate, therefore the whole utility is taken as $P \\cdot Q -\\mathcal{R}(P; M)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0556","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"}