Sarang Gopalakrishnan: Phases of Local Inference

The quantum error correction threshold is part of a much larger family of phase transitions in the structure of mixed states (or classical probability distributions); these are transitions in whether the state can be locally recovered if part of it is lost. I will introduce a diagnostic for such mixed-state phase transitions, the "Markov length" associated with the conditional mutual information, and discuss some counterintuitive properties of how the Markov length evolves under stochastic dynamics -- for example, it diverges when one heats an ordered state. I will argue that a finite-time inference phase transition occurs even in a simple classical model of hardcore diffusing particles in two or more dimensions.