Stability of Quantum LDPC States under Local Pauli Noise
Abstract
Quantum low-density parity-check (qLDPC) codes have a canonical mixed state---the normalized projector onto the code space---that lies at the intersection of quantum error correction and quantum many-body physics, yet the stability of its information-theoretic structure under local noise remains poorly understood. Recent progress on mixed-state phases of matter has identified the spatial decay of conditional mutual information (CMI) I(A:C|B) as a key diagnostic of such stability, analogous to the role of the spectral gap for quantum ground states. We prove that, for the normalized code-projector state of a ℤd qLDPC stabilizer code under local Pauli noise, the CMI across a buffer B separating A from C decays exponentially with the width of B in two complementary noise regimes independent of system size. At weak noise, this holds for full-system tripartitions, where correlations between the two sides require an error cluster to cross the buffer, an exponentially unlikely event. At strong noise, exponential decay holds whenever the buffer supports no logical operator, since correlations can persist only along rare chains of buffer qudits that remain informative. Under an additional space-uniformity assumption, we establish the robustness of Levin--Wen topological entropy. On finite-dimensional lattices of size n, the weak-noise bound further implies a constant-layer quasi-local Petz recovery channel of range O(poly(log n)/ε) that recovers the noiseless state within trace-distance error ε. Both CMI bounds apply to general qLDPC interaction graphs, including geometries where such constant-depth quasi-local recovery need not exist. Thus, the exponential decay of the noise-induced CMI provides a general criterion for mixed-state phase stability.
Related
- Characterizing Local and Correlated Pauli Noise in Quantum Teleportation Circuits
- Bounding Fidelity of Non-Stabilizer States from Local Pauli Measurements
- Pauli-ball discrepancy and stability of quantum codes
- Scalable Exact Non-Pauli Noise Simulation for Fault-Tolerant Quantum Circuits
- Orientation-dependent Pauli noise in one-dimensional discrete-time quantum walks
BibTeX
@misc{yang2026stability,
title = {{Stability of Quantum LDPC States under Local Pauli Noise}},
author = {Tai-Hsuan Yang and Andrew D. Kim and Akash Vijay and Jong Yeon Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22357},
eprint = {2610.22357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22357},
}
RIS
TY - UNPB
TI - Stability of Quantum LDPC States under Local Pauli Noise
AU - Tai-Hsuan Yang
AU - Andrew D. Kim
AU - Akash Vijay
AU - Jong Yeon Lee
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22357
UR - https://arxiv.org/abs/2610.22357
AB - Quantum low-density parity-check (qLDPC) codes have a canonical mixed state---the normalized projector onto the code space---that lies at the intersection of quantum error correction and quantum many-body physics, yet the stability of its information-theoretic structure under local noise remains poorly understood. Recent progress on mixed-state phases of matter has identified the spatial decay of conditional mutual information (CMI) I(A:C|B) as a key diagnostic of such stability, analogous to the role of the spectral gap for quantum ground states. We prove that, for the normalized code-projector state of a ℤ_d qLDPC stabilizer code under local Pauli noise, the CMI across a buffer B separating A from C decays exponentially with the width of B in two complementary noise regimes independent of system size. At weak noise, this holds for full-system tripartitions, where correlations between the two sides require an error cluster to cross the buffer, an exponentially unlikely event. At strong noise, exponential decay holds whenever the buffer supports no logical operator, since correlations can persist only along rare chains of buffer qudits that remain informative. Under an additional space-uniformity assumption, we establish the robustness of Levin--Wen topological entropy. On finite-dimensional lattices of size n, the weak-noise bound further implies a constant-layer quasi-local Petz recovery channel of range O(poly(log n)/ε) that recovers the noiseless state within trace-distance error ε. Both CMI bounds apply to general qLDPC interaction graphs, including geometries where such constant-depth quasi-local recovery need not exist. Thus, the exponential decay of the noise-induced CMI provides a general criterion for mixed-state phase stability.
ER -