Amirreza Negari

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Criticality in quantum many-body systems is usually tied to scale-invariant correlations in pure states; mixed states lack a comparable organizing principle. Here we introduce critical mixed-state phases, in which the conditional mutual information (CMI) decays with a diverging length scale across the entire phase. We realize two such phases by applying coherent (invertible) noise to topological memories : (i) a classical memory subjected to coherent Pauli shuffle noise, where we analytically establish critical CMI scaling via a statistical-mechanical mapping; and (ii) a quantum memory (surface code) subjected to coherent Z rotations, where large-scale numerics reveal a stable phase with divergent Markov length and long-range entanglement. A unified picture emerges by mapping CMI to transport physics and the conductance of a Chalker-Coddington network, identifying the critical phase with a metallic regime. We further discuss implications for error correction: the critical phase is information-theoretically correctable yet admits no finite-depth local decoder, whereas local decoders exist away from criticality.

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Perimeter Institute
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Contact: Simon Trebst