Can One Validly Use Classical Statistical Inference in Open Quantum Systems?

A major problem to perform statistical inference in open quantum systems is the perturbation induced by the measurement process. However, at least theoretically, a suitable choice of the measurement process could provide a consistent approach through classical stochastic processes. This work proposes a method to perform statistical inference on open quantum systems represented by quantum Markov semigroups having a suitable classical reduction. The method is based on measurements associated to observables generating invariant abelian algebras.