{"paper":{"title":"Entropy on Spin Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Peter Harremo\\\"es","submitted_at":"2017-07-11T11:28:24Z","abstract_excerpt":"Recently it has been demonstrated that the Shannon entropy or the von Neuman entropy are the only entropy functions that generate a local Bregman divergences as long as the state space has rank 3 or higher. In this paper we will study the properties of Bregman divergences for convex bodies of rank 2. The two most important convex bodies of rank 2 can be identified with the bit and the qubit. We demonstrate that if a convex body of rank 2 has a Bregman divergence that satisfies sufficiency then the convex body is spectral and if the Bregman divergence is monotone then the convex body has the sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03222","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"}