Data-certified mixing-rate bounds and GKLS identification from one-step channels

Many tasks in open quantum systems and quantum information theory require guarantees on the mixing rate of a continuous-time Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) semigroup, while experimental access is typically limited to a discrete one-step completely positive trace-preserving (CPTP) map estimated from data. We provide an operational route from such one-step information to certified lower bounds on exponential mixing rates and to a compatible Lindblad generator. Given a statistically consistent estimate of a stationary channel E_delta t and one stationary state tau, we first certify a Doeblin minorization mass for E_delta t and translate it into a data-certified contraction rate gamma_op in trace distance. A Chernoff-type telescoping argument then controls the embedding error between discrete dynamics and any continuous-time realization, showing that the same rate holds up to an O(t Delta t) correction. Finally, we recover a GKLS generator by a convex semidefinite log-projection onto the generator cone, constrained to be consistent with the observed invariant state and the certificate. The resulting guarantee is non-asymptotic, depends only on observed counts and one stationary state, and bridges classical Doeblin theory with data-driven identification of quantum Markov semigroups from one-step CPTP experiments.