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pith:MGWAO3HY

pith:2026:MGWAO3HY5DMZWHOMNAZYZQRCMD
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Mixed-State Long-Range Entanglement from Dimensional Constraints

Leonardo A. Lessa, Tsung-Cheng Lu

Maximally mixed states on translation-invariant subspaces of a 1D ring are long-range entangled due to subspace dimension mismatch.

arxiv:2605.15201 v1 · 2026-05-14 · quant-ph · cond-mat.stat-mech · cond-mat.str-el

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Internet Archive 1 capture
2026-05-17 22:23:38 · view Wayback capture · all captures · memento
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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

62 extracted · 62 resolved · 2 Pith anchors

[1] M. B. Hastings, Topological order at nonzero temperature, Phys. Rev. Lett.107, 210501 (2011) 2011
[2] L. A. Lessa, M. Cheng, and C. Wang, Mixed-state quan- tum anomaly and multipartite entanglement, Phys. Rev. X15, 011069 (2025) 2025
[3] 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] 2024
[4] 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) 2024
[5] Sun, Anomalous matrix product operator symmetries and 1d mixed-state phases (2025), arXiv:2504.16985 [quant-ph] 2025

Formal links

2 machine-checked theorem links

Receipt and verification
First computed 2026-05-17T21:40:24.930488Z
Last reissued 2026-05-18T12:28:38.357277Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

61ac076cf8e8d99b1dcc68338cc22260df2550aef08c8069b0f61fdb7aa2371d

Aliases

arxiv: 2605.15201 · arxiv_version: 2605.15201v1 · doi: 10.48550/arxiv.2605.15201 · pith_short_12: MGWAO3HY5DMZ · pith_short_16: MGWAO3HY5DMZWHOM · pith_short_8: MGWAO3HY
Agent API
Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/MGWAO3HY5DMZWHOMNAZYZQRCMD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 61ac076cf8e8d99b1dcc68338cc22260df2550aef08c8069b0f61fdb7aa2371d
Canonical record JSON
{
  "metadata": {
    "abstract_canon_sha256": "f617de8ec97fe92a9b50cc697ed39388ff63922bd71cfc855bb4f43a3c602fdb",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cond-mat.str-el"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-14T17:59:59Z",
    "title_canon_sha256": "bb8a51666dc4b47de73d8a109554800164809cdbf8e326515438dc13823087b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15201",
    "kind": "arxiv",
    "version": 1
  }
}