Measures of Chirality in Mixed-State Topological Phases
Abstract
What does it mean for a mixed-state topological phase to be chiral? Mathematically, chirality can be sharply characterized through the symmetry algebra of the mixed state. Physically, however, the question is far more subtle. In pure states, chirality in topological phase is tied to a web of familiar diagnostics, involving bulk-boundary correspondence, a gapless entanglement spectrum, a nontrivial modular commutator, and a quantized thermal Hall response. We show that none of these diagnostics remain reliable in mixed states. Instead, for decohered topological phases with a known error-free parent state, we propose two relative-entropy-based measures that can diagnose chirality, with one of them further extracting the chiral central charge. As a concrete example, we use these measures to analyze the em2-decohered ℤ3 toric code, identifying the chirality transition to be in the random-bond Potts class for the particle-hole symmetric channel, and the polarized random bond Potts class for asymmetric channels. Our results emphasize how mixed-state topology demands intrinsically new diagnostics beyond direct analogues of pure-state probes.
Related
- Topological Mixed States: Phases of Matter from Axiomatic Approaches
- Mixed-State Phases from Local Reversibility
- Mixed-state phases induced by power-law quantum channels
- Tensor network representations for intrinsically mixed-state topological orders
- Mixed state entanglement measures for open string geometry
BibTeX
@misc{sun2026measures,
title = {{Measures of Chirality in Mixed-State Topological Phases}},
author = {Shijun Sun and Bader Aldossari and Rasmit Devkota and Zhu-Xi Luo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.26235},
eprint = {2606.26235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26235},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Measures of Chirality in Mixed-State Topological Phases
AU - Shijun Sun
AU - Bader Aldossari
AU - Rasmit Devkota
AU - Zhu-Xi Luo
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2606.26235
UR - https://arxiv.org/abs/2606.26235
AB - What does it mean for a mixed-state topological phase to be chiral? Mathematically, chirality can be sharply characterized through the symmetry algebra of the mixed state. Physically, however, the question is far more subtle. In pure states, chirality in topological phase is tied to a web of familiar diagnostics, involving bulk-boundary correspondence, a gapless entanglement spectrum, a nontrivial modular commutator, and a quantized thermal Hall response. We show that none of these diagnostics remain reliable in mixed states. Instead, for decohered topological phases with a known error-free parent state, we propose two relative-entropy-based measures that can diagnose chirality, with one of them further extracting the chiral central charge. As a concrete example, we use these measures to analyze the em^2-decohered ℤ_3 toric code, identifying the chirality transition to be in the random-bond Potts class for the particle-hole symmetric channel, and the polarized random bond Potts class for asymmetric channels. Our results emphasize how mixed-state topology demands intrinsically new diagnostics beyond direct analogues of pure-state probes.
ER -