Critical non-equilibrium phases from noisy topological memories

• URL: http://arxiv.org/abs/2601.10792v1
• Date: Thu, 15 Jan 2026 19:00:04 GMT
• Title: Critical non-equilibrium phases from noisy topological memories
• Authors: Amir-Reza Negari, Subhayan Sahu, Jan Behrends, Benjamin Béri, Timothy H. Hsieh,
• Abstract summary: We show the existence of an extended non-equilibrium critical phase, characterized by sub-exponential decay of conditional mutual information.<n>We find that the critical phase retains partial logical information that can be recovered by a global decoder, but not by any quasi-local decoder.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We demonstrate the existence of an extended non-equilibrium critical phase, characterized by sub-exponential decay of conditional mutual information (CMI), in the surface code subject to heralded random Pauli measurement channels. By mapping the resulting mixed state to the ensemble of completely packed loops on a square lattice, we relate the extended phase to the Goldstone phase of the loop model. In particular, CMI is controlled by the characteristic length scale of loops, and we use analytic results of the latter to establish polylogarithmic decay of CMI in the critical phase. We find that the critical phase retains partial logical information that can be recovered by a global decoder, but not by any quasi-local decoder. To demonstrate this, we introduce a diagnostic called punctured coherent information which provides a necessary condition for quasi-local decoding.

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