A Possible Time-Dependent Generalization of the Bipartite Quantum Marginal Problem

In this work, we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced states (marginals). The compatibility of such choice with a global unitary evolution is considered. For the nonunitary case, we propose a systematic method to reconstruct examples of master equations and address them to different physical scenarios.