DETECTING PRIOR-DATA CONFLICT IN QUANTUM STATE ESTIMATION

Abstract

This work concerns the check for prior-data conflict in quantum experiments. A prior-data conflict occurs when the prior places most of its weight in regions of the parameter space that the data suggests are unfeasible. Such a conflict could indicate that the prior was poorly chosen, or that the experiment has not been behaving as expected. In quantum measurements, the marginal likelihood, an important quantity in checking for prior-data conflict, is generally computationally difficult to evaluate. We developed tools for sampling from the quantum state space, a necessity for the rest of this work. We also investigated the feasibility of performing prior-data conflict checks on quantum problems using the marginal likelihood as a measure of typicality of the data. Subsequently, we explore other checking methods that may be more suited for quantum problems, considering sensitivity of the tests as well as computational tractability.