{"paper":{"title":"R\\'{e}nyi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Ikuo Ichinose, Takahiro Orito, Yoshihito Kuno","submitted_at":"2025-05-04T14:15:03Z","abstract_excerpt":"Discovering and classifying non-trivial mixed states and mixed state phase transitions are some of the most important current issues in condensed matter and quantum information. In this study, we investigate some non-trivial mixed states and phase transitions between them by using the second R\\'{e}nyi conditional mutual information (CMI). The CMI can measure mixed state ``gap'', estimated by the exponential decay rate of the second R\\'{e}nyi CMI under a tripartition of system, which provides the second R\\'{e}nyi version of the Markov length. We introduce an efficient numerical scheme for the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02125","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/2505.02125/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"}