{"paper":{"title":"Duality of reduced density matrices and their eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Christian Schilling, Rolf Schilling","submitted_at":"2014-08-13T20:07:05Z","abstract_excerpt":"For states of quantum systems of $N$ particles with harmonic interactions we prove that each reduced density matrix $\\rho$ obeys a duality condition. This condition implies duality relations for the eigenvalues $\\lambda_k$ of $\\rho$ and relates a harmonic model with length scales $l_1,l_2, \\ldots, l_N $ with another one with inverse lengths $1/l_1, 1/l_2,\\ldots, 1/l_N$. Entanglement entropies and correlation functions inherit duality from $\\rho$. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3128","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":""},"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"}