Information Critical Phases under Decoherence

• URL: http://arxiv.org/abs/2512.22121v1
• Date: Fri, 26 Dec 2025 18:59:49 GMT
• Title: Information Critical Phases under Decoherence
• Authors: Akash Vijay, Jong Yeon Lee,
• Abstract summary: Quantum critical phases are extended regions of phase space characterized by a diverging correlation length.<n>We demonstrate that such a phase arises in decohered $mathbbZ_N$ Toric codes by assessing both the CMI and the coherent information.<n>Our findings identify a gapless analog for mixed-state phases that still acts as a fractional topological quantum memory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an information critical phase as an extended region of a mixed state phase diagram where the Markov length, the characteristic length scale governing the decay of the conditional mutual information (CMI), diverges. We demonstrate that such a phase arises in decohered $\mathbb{Z}_{N}$ Toric codes by assessing both the CMI and the coherent information, the latter quantifying the robustness of the encoded logical qudits. For $N>4$, we find that the system hosts an information critical phase intervening between the decodable and non-decodable phases where the coherent information saturates to a fractional value in the thermodynamic limit, indicating that a finite fraction of logical information is still preserved. We show that the density matrix in this phase can be decomposed into a convex sum of Coulombic pure states, where gapped anyons reorganize into gapless photons. We further consider the ungauged $\mathbb{Z}_{N}$ Toric code and interpret its mixed state phase diagram in the language of strong-to-weak spontaneous symmetry breaking. We argue that in the dual model, the information critical phase arises because the spontaneously broken off-diagonal $\mathbb{Z}_{N}$ symmetry gets enhanced to a U(1) symmetry, resulting in a novel superfluid phase whose gapless modes involve coherent excitations of both the system and the environment. Finally, we propose an optimal decoding protocol for the corrupted $\mathbb{Z}_{N}$ Toric code and evaluate its effectiveness in recovering the fractional logical information preserved in the information critical phase. Our findings identify a gapless analog for mixed-state phases that still acts as a fractional topological quantum memory, thereby extending the conventional paradigm of quantum memory phases.

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