Long-range entangled criticality from coherent errors
Abstract
We find that coherent error can induce a phase transition from the clean surface code phase into an extended long-range entangled critical regime with diverging Markov length. To demonstrate this, we establish two general results of independent interest. The first relates topology and quantum information to mixed-state entanglement: we show that when a noise channel acting on a topological code preserves a higher-form symmetry and nonzero coherent information, the noisy state for generic logical input is long-range entangled. The second generalizes the local recovery construction based on finite Markov length to any locally parameterized family, thus encompassing local Lindbladian evolution, coherent errors followed by syndrome dephasing, and thermal states. We apply these results to the honeycomb surface code, in which we find an extended long-range entangled critical regime that is a quasi-long-ranged counterpart of 1-form strong-to-weak spontaneous symmetry breaking. As a byproduct of these studies, we relate the conditional mutual information to conductance in a Majorana network model.
Related
- Quantum teleportation with partially entangled joint measurements induced by coherent errors
- Criticality of nonreciprocal phase oscillators with long-range interactions
- Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions
- Coherent errors, syndrome extraction and the Robustness of Magic in stabiliser codes
- Code-Visible Liouvillian Modes and Coherent Logical Errors in Quantum Codes
BibTeX
@misc{negari2026longrange,
title = {{Long-range entangled criticality from coherent errors}},
author = {Amir-Reza Negari and Subhayan Sahu and Jan Behrends and Benjamin Béri and Timothy H. Hsieh},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03811},
eprint = {2611.03811},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03811},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-range entangled criticality from coherent errors
AU - Amir-Reza Negari
AU - Subhayan Sahu
AU - Jan Behrends
AU - Benjamin Béri
AU - Timothy H. Hsieh
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03811
UR - https://arxiv.org/abs/2611.03811
AB - We find that coherent error can induce a phase transition from the clean surface code phase into an extended long-range entangled critical regime with diverging Markov length. To demonstrate this, we establish two general results of independent interest. The first relates topology and quantum information to mixed-state entanglement: we show that when a noise channel acting on a topological code preserves a higher-form symmetry and nonzero coherent information, the noisy state for generic logical input is long-range entangled. The second generalizes the local recovery construction based on finite Markov length to any locally parameterized family, thus encompassing local Lindbladian evolution, coherent errors followed by syndrome dephasing, and thermal states. We apply these results to the honeycomb surface code, in which we find an extended long-range entangled critical regime that is a quasi-long-ranged counterpart of 1-form strong-to-weak spontaneous symmetry breaking. As a byproduct of these studies, we relate the conditional mutual information to conductance in a Majorana network model.
ER -