Pith Number

pith:GWYVOHQV

pith:2023:GWYVOHQV7ZQOCBY3IUWFYUCWXV

not attested not anchored not stored refs resolved

Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions

Ashvin Vishwanath, Ehud Altman, Ruihua Fan, Yimu Bao

Decoherence on abelian topological states is a temporal defect in the doubled TQFT that drives anyon condensation transitions classifying mixed-state phases and information loss by Lagrangian subgroups.

arxiv:2301.05687 v2 · 2023-01-13 · quant-ph · cond-mat.str-el

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GWYVOHQV7ZQOCBY3IUWFYUCWXV}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The decoherence-induced phases and the loss of quantum information are classified by the Lagrangian subgroups of the double topological order. Our framework generalizes the error recovery transitions, previously derived for certain stabilizer codes, to generic topologically ordered states and shows that they stem from phase transitions in the intrinsic topological order characterizing the mixed state.

C2weakest assumption

That decoherence on the density matrix of an abelian topologically ordered state can be faithfully represented as a temporal defect inserted into the doubled topological quantum field theory that describes the pure state (abstract, paragraph 2).

C3one line summary

Decoherence on abelian topological order is modeled as a temporal defect in double TQFT driving boundary anyon condensation transitions classified by Lagrangian subgroups of the doubled order.

References

65 extracted · 65 resolved · 27 Pith anchors

[2] (Incoherent error) [ 1, 1,−1,−1]T ·m = 0 mod K(2)Λ,∀m∈M[49]. Here, θml := 2πmT (K(2))−1l characterizes the mutual statistics between two anyons. In three examples, the Toric code, double semion model

[3] Semeghiniet al., Probing topological spin liquids on a programmable quantum simulator, Science374, abi8794 (2021), arXiv:2104.04119 [quant-ph] 2021

[4] Bluvsteinet al., A quantum processor based on co- herent transport of entangled atom arrays, Nature604, 451 (2022), arXiv:2112.03923 [quant-ph] 2022

[5] K. J. Satzinger et al. , Realizing topologically ordered states on a quantum processor, Science 374, abi8378 (2021), arXiv:2104.01180 [quant-ph] 2021

[6] Acharya et al 2022

Cited by

15 papers in Pith

Invariants of Sequential Circuits and Generalized Non-Abelian Statistics

Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions

Topologically Ordered Steady States in Open Quantum Systems

Steady-state topological order

Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak

Receipt and verification

First computed	2026-06-02T03:05:03.072525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35b1571e15fe60e1071b452c5c5056bd5f560c283c26ebb891ddcdacc210726d

Aliases

arxiv: 2301.05687 · arxiv_version: 2301.05687v2 · doi: 10.48550/arxiv.2301.05687 · pith_short_12: GWYVOHQV7ZQO · pith_short_16: GWYVOHQV7ZQOCBY3 · pith_short_8: GWYVOHQV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GWYVOHQV7ZQOCBY3IUWFYUCWXV \
  | 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: 35b1571e15fe60e1071b452c5c5056bd5f560c283c26ebb891ddcdacc210726d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f31afd999d5eaac8465e92d15ba7976109f05e3e5fd072e20566b84849900d7f",
    "cross_cats_sorted": [
      "cond-mat.str-el"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2023-01-13T18:15:04Z",
    "title_canon_sha256": "7c22728e26c78aaf805ae2b2a0d7b58091072aaaf5660622967109ce61e0be99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2301.05687",
    "kind": "arxiv",
    "version": 2
  }
}