Emergent random matrix universality in Kraus maps of chaotic quantum dynamics

We study the ensemble of Kraus operators on a small subsystem in quantum many-body chaotic dynamics without conservation laws, generated by projective measurements on its bath. These Kraus operators effectively unravel the quantum channel acting on the subsystem. We show that at late times the collection of Kraus operators are distributed according to the complex Ginibre (GinUE) ensemble, while at intermediate times an additional random log-normal rescaling appears in their distribution, with its parameters determined by the bath size and circuit depth. Numerics of various 1D circuit models confirm these behaviors, which we capture by a family of universal Ansatz. These findings provide a dynamical mechanism for "deep thermalization", a form of equilibration that goes beyond the thermalization of local observables. We further explore quantum-information-theoretic consequences: the subsystem's reduced dynamics leaks asymptotically minimal information into the bath and form approximate unitary designs, suggesting recoverability of information. Our results bridge emergent universality in many-body dynamics with quantum-information perspectives on error correction.