{"paper":{"title":"Isospectral majorization and isoperimetric inequalities for coherent states on the Bloch sphere","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.CA","math.FA","math.MP"],"primary_cat":"quant-ph","authors_text":"Luis Daniel Abreu","submitted_at":"2026-08-12T16:46:26Z","abstract_excerpt":"Let $\\mathcal{P}_{N}$ be the $(N+1)$-dimensional Hilbert space of analytic polynomials of degree at most $N$. This is the natural environment to define $SU(2)$ (Bloch) coherent states. Let $Q_{\\rho }$ be the Husimi function of a density operator $\\rho $ on $% \\mathcal{P}_{N}$. We prove an isospectral version of Lieb-Solovej inequality: if $\\rho ^{\\downarrow }$ is obtained by placing the eigenvalues of $\\rho $ in decreasing order along the monomial basis, then \\begin{equation*} \\int_{\\mathbb{C}}\\Phi (Q_{\\rho }(z))\\,dm(z)\\leq \\int_{\\mathbb{C}}\\Phi (Q_{\\rho ^{\\downarrow }}(z))\\,dm(z) \\end{equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12248","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/2608.12248/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"}