We address the problem of efficiently and effectively compress density operators (DOs), by providing an efficient procedure for learning the most likely DO, given a chosen set of partial information.We explore, in the context of quantum information theory, the generalisation of the maximum Handbags and Wallets » Cross Body Purses entropy estimator for DOs, when the direct dependencies between the subsystems are provided.As a preliminary analysis, we restrict the problem to tripartite systems when two marginals are known.When the marginals are compatible with the existence of a quantum Markov chain (QMC) we show that there exists a recovery procedure for the maximum entropy estimator, and moreover, that for these states many well-known classical results follow.Furthermore, we notice that, contrary to the classical case, two marginals, compatible with some tripartite state, might not be compatible with a QMC.
Finally, we provide AFTER SUN SOOTHER a new characterisation of quantum conditional independence in light of maximum entropy updating.At this level, all the Hilbert spaces are considered finite dimensional.