{"paper":{"title":"Positive definite matrices with Hermitian blocks and their partial traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eun-Young Lee, Jean-Christophe Bourin, Minghua Lin","submitted_at":"2012-08-31T13:41:27Z","abstract_excerpt":"Let $H$ be a positive semi-definite matrix partitioned in $\\beta\\times \\beta$ Hermitian blocks,  $H=[A_{s,t}]$, $1\\le s,t,\\le \\beta$.  Then, for all symmetric  norms,\n{equation*}\n\\| H \\| \\le \\| \\sum_{s=1}^{\\beta} A_{s,s} \\|.\n{equation*}\nThe proof uses a nice decomposition   for positive   matrices   and unitary congruences with the generators of a Clifford algebra.   A few corollaries are given, in particular the partial trace operation increases norms of separable states on a real Hilbert space, leading to a  conjecture for  usual complex Hilbert spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6494","kind":"arxiv","version":3},"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"}