{"paper":{"title":"Triangle inequalities in coherence measures and entanglement concurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chengjie Zhang, Wenlong You, Yue Dai, Yuli Dong","submitted_at":"2018-04-11T07:18:29Z","abstract_excerpt":"We provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-$2$ state $\\varrho$ can be expressed as a convex combination of two pure states, i.e., $\\varrho=p_{1}|\\psi_{1}\\rangle\\langle\\psi_{1}|+p_{2}|\\psi_{2}\\rangle\\langle\\psi_{2}|$, a triangle inequality can be established as $\\big{|}E(|\\Psi_{1}\\rangle)-E(|\\Psi_{2}\\rangle)\\big{|}\\leq E(\\varrho)\\leq E(|\\Psi_{1}\\rangle)+E(|\\Psi_{2}\\rangle)$, where $|\\Psi_{1}\\rangle=\\sqrt{p_{1}}|\\psi_{1}\\rangle$ and $|\\Psi_{2}\\rangle=\\sqrt{p_{2}}|\\psi_{2}\\rangle$, $E$ can be considered either coherence measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03840","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"}