{"paper":{"title":"A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Lu wei","submitted_at":"2017-06-26T00:59:54Z","abstract_excerpt":"It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\\leq n$ is given by \\begin{equation*} -\\psi_{1}\\left(mn+1\\right)+\\frac{m+n}{mn+1}\\psi_{1}\\left(n\\right)-\\frac{(m+1)(m+2n+1)}{4n^{2}(mn+1)}, \\end{equation*} where $\\psi_{1}(\\cdot)$ is the trigamma function. We give a proof of this formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08199","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"}