Anasuya Lyons
Recent studies have shown that the interplay between unitary dynamics and projective measurements leads to a novel phase transition characterized by the dynamics of quantum entanglement, entropy, and the Fisher information. In this work, we study a classical analogue of the phase transition by investigating random classical circuits interspersed by bit-erasure errors in one dimension. We find evidence of a phase transition from an “encoding” to a “non-encoding” phase above a critical error rate. In the encoding phase, a nonzero amount of Shannon entropy per bit can be retained in the system, indicating at least a subset of initially encoded information is protected from errors. In contrast, in the non-encoding phase, the Shannon entropy approaches zero within a finite circuit depth independent of system sizes. We extract the phase transition point and the dynamical scaling exponents near the transition point using numerical simulations. Furthermore, we develop an exact method to map the average behavior of the classical circuit dynamics to an infectious disease model, providing a new framework to study universal aspects in the dynamics of classical information.