Self-restricting Noise in Quantum Dynamics

States of open quantum systems usually decay continuously under environmental interactions. Quantum Markov semigroups model such processes in dissipative environments. It is known that a finite-dimensional quantum Markov semigroup with detailed balance induces exponential decay toward a subspace of invariant or fully decayed states, under what are called modified logarithmic Sobolev inequalities. We analyze continuous processes that combine coherent and stochastic processes, breaking detailed balance. We find counterexamples to analogous decay bounds for these processes. Through analogs of the quantum Zeno effect, noise can suppress interactions that would spread it. Faster decay of a subsystem may thereby slow overall decay. Hence the relationship between the strength of noise on a part and induced decay on the whole system is often non-monotonic. We observe this interplay numerically and its discrete analog experimentally on IBM Q systems. Our main results then explain and generalize the phenomenon theoretically. In contrast, we also lower bound decay rates above any given timescale by combining estimates for simpler, effective processes across times.