Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics

In this study, we explore the information capacity of open quantum systems, focusing on the effective channels formed by the subsystem of random quantum circuits and quantum Hamiltonian evolution. By analyzing the subsystem information capacity, which is closely linked to quantum coherent information of these effective quantum channels, we uncover a diverse range of dynamical and steady behaviors depending on the types of evolution. Therefore, the subsystem information capacity serves as a valuable tool for studying the intrinsic nature of various dynamical phases, such as integrable, localized, thermalized, and topological systems. We also reveal the impact of different initial information encoding schemes on information dynamics including one-to-one, one-to-many, and many-to-many. To support our findings, we provide representative examples for numerical simulations, including random quantum circuits with or without mid-circuit measurements, random Clifford Floquet circuits, free and interacting Aubry-Andr\'e models, and Su-Schrieffer-Heeger models. These numerical results are further quantitatively explained using the effective statistical model mapping and the quasiparticle picture in the cases of random circuits and non-interacting Hamiltonian dynamics, respectively.