{"paper":{"title":"Standard symmetrized variance with applications to coherence, uncertainty and entanglement","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lin Zhang, Ming-Jing Zhao, Shao-Ming Fei","submitted_at":"2022-07-13T08:43:59Z","abstract_excerpt":"Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state and call it the symmetrized variance. Moreover we work out the analytical expression of the symmetrized variance and find that such expression is in the factorized form where two factors separately depends on the diagonal observable and quantum state. By shifting the factor corresponding to the diagonal observable, we introduce the notion named the standard symmetrize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.06048","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/2207.06048/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"}