Quantum-state diffusion: Application to Bayesian hierarchical modeling

The geometrical interpretation of density operators for open quantum system is investigated. After the discussion of stochastic mapping and the purifying lifts of curves of density matrices, the quantum analog of the classical recipe for the construction of an infinitesimal generator has been established. Despite the main contribution of the present paper in providing the formal expression of such generator, a simple experimental realization of a geometrically intuitive approach to variational inference also established. Nonetheless, the numerical results given here are competitive with those from the other methods used for quantum and classical systems and provide insight into the origin of properties of open quantum systems. •Implication of stochastic Liouvillian operator to evaluate an integral over the unitary group.•Bayesian interpretation of the eigenvalue problem for dynamical systems.•Quantum jump proposals for the Monte Carlo scheme in Bayesian inferential methodology.•Probability measures on the set of density matrices.