{"paper":{"title":"Mixed-State Long-Range Entanglement from Dimensional Constraints","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"Maximally mixed states on translation-invariant subspaces of a 1D ring are long-range entangled due to subspace dimension mismatch.","cross_cats":["cond-mat.stat-mech","cond-mat.str-el"],"primary_cat":"quant-ph","authors_text":"Leonardo A. Lessa, Tsung-Cheng Lu","submitted_at":"2026-05-14T17:59:59Z","abstract_excerpt":"We present a new mechanism for long-range entanglement (LRE) in strongly symmetric many-body mixed states that does not rely on symmetry anomalies or long-range correlations. Our primary example is the maximally mixed state in the translation-invariant subspace on a one-dimensional ring. This state is LRE because translationally symmetric short-range entangled states span a subspace whose dimension grows only polynomially with system size, whereas the full translation-invariant subspace grows exponentially. We further discuss certain unconventional properties of this state, including logarithm"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This state is LRE because translationally symmetric short-range entangled states span a subspace whose dimension grows only polynomially with system size, whereas the full translation-invariant subspace grows exponentially.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the dimension of the translationally symmetric short-range entangled subspace grows only polynomially with system size while the full translation-invariant subspace grows exponentially, and that this dimensional mismatch directly implies long-range entanglement in the maximally mixed state.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Maximally mixed states on translation-invariant subspaces of a 1D ring are long-range entangled due to subspace dimension mismatch.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cfc1ecfe47e9ed88c4a79934ae2f6f5215f3c22415f74ffb3da545dd31b6d4cf"},"source":{"id":"2605.15201","kind":"arxiv","version":1},"verdict":{"id":"ed3d975e-958d-4c7d-83a4-675209b204f4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:00:35.201685Z","strongest_claim":"This state is LRE because translationally symmetric short-range entangled states span a subspace whose dimension grows only polynomially with system size, whereas the full translation-invariant subspace grows exponentially.","one_line_summary":"The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the dimension of the translationally symmetric short-range entangled subspace grows only polynomially with system size while the full translation-invariant subspace grows exponentially, and that this dimensional mismatch directly implies long-range entanglement in the maximally mixed state.","pith_extraction_headline":"Maximally mixed states on translation-invariant subspaces of a 1D ring are long-range entangled due to subspace dimension mismatch."},"references":{"count":62,"sample":[{"doi":"","year":2011,"title":"M. B. Hastings, Topological order at nonzero temperature, Phys. Rev. Lett.107, 210501 (2011)","work_id":"ebf61235-7c29-4099-93f1-7477270c2564","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"L. A. Lessa, M. Cheng, and C. Wang, Mixed-state quan- tum anomaly and multipartite entanglement, Phys. Rev. X15, 011069 (2025)","work_id":"008ba7a0-04b5-4701-97e9-852a0a6b8385","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Z. Wang and L. Li, Anomaly in open quantum systems and its implications on mixed-state quantum phases (2024), arXiv:2403.14533 [cond-mat, physics:math-ph, physics:quant-ph]","work_id":"134580bc-9939-472f-86bd-56b34e4a413a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"A. Ruiz-de-Alarc´ on, J. Garre-Rubio, A. Moln´ ar, and D. P´ erez-Garc´ ıa, Matrix product operator algebras II: Phases of matter for 1D mixed states, Letters in Mathe- matical Physics114, 43 (2024)","work_id":"e0959ab0-1e3d-4671-8de7-8edfc7bd12bf","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Sun, Anomalous matrix product operator symmetries and 1d mixed-state phases (2025), arXiv:2504.16985 [quant-ph]","work_id":"14f6ed44-5baa-4042-ae5d-672707877f10","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":62,"snapshot_sha256":"34c9f95f3438ba6dd1e6027d9f5202a9c1e2e80f46422ece50f4160d72d1a5b0","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a50d3aa21c7762cbc263fbb12033c96e480efb7535d2b9f199845dfb640730dd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}