Purification and scrambling in a chaotic Hamiltonian dynamics with measurements

Chaotic transverse-field Ising model with measurements exhibits interesting purification dynamics. Ensemble of non-unitary dynamics a chaotic many-body system phase transition. We numerically find that the law increase purity changes by projective in model. In order to study this behavior detail, we construct formalism tripartite mutual information (TMI) for time evolution operator using state-channel map. The numerical result saturation value TMI indicates existence measurement-induced This implies two distinct phases, mixed and purified phase. Furthermore, real-space spread is investigated explore spatial patterns spreading. Even phase, pattern light cone quantum not deformed, but its density propagation reduced on average measurements. also distinguishes integrable regimes system.