Measurement-induced phase transitions (MIPT) were discovered for chaotic random quantum model undergoing projective or continuous measurements. In these models, depending on the rate of measurement, the system is either in an entangling phase or disentangling phase. The existence of MIPT was first demonstrated for quantum systems using quantities such as entanglement or Rényi entropy for the characterization of the phase transition. In this talk, I will present a classical model showing the same phenomenology which consists of a single random walker undergoing continuous weak measurement. Importantly, our approach relies on an analytical map in the weak/short time regime between the probability distribution of our model and the interface height of the Kardar-Parisi-Zhang equation which unveils an unexpected connection between the physics of interface growth and information theory.

* Tony Jin: University of Chicago