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arXiv · 2507.02292

Mixed-state phases from local reversibility

Shengqi Sang·Leonardo A. Lessa·Roger S. K. Mong·Tarun Grover·Chong Wang·Timothy H. Hsieh
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Abstract

We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a new generalization of symmetry for open quantum systems. For abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has non-trivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.

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Shengqi Sang, Leonardo A. Lessa, Roger S. K. Mong, Tarun Grover, Chong Wang, Timothy H. Hsieh. 2025-07-03. Mixed-state phases from local reversibility. https://arxiv.org/abs/2507.02292

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