2025/12/26 by Akash Vijay, Jong Yeon Lee, Vijay, Akash +1
Computer Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2512.22121
openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
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 ℤN 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 ℤN 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 ℤN 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 ℤN 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.