Matthew Leifer, University College London
Abstract
Quantum theory can be thought of a noncommutative generalization of classical probability and, from this perspective, it is puzzling that no quantum generalization of conditional probability is in widespread use. In this talk, I discuss one such generalization and show how it can unify the description of ensemble preparations of quantum states, POVM measurements and the description of correlations between quantum systems. The conditional states formalism allows for a description of prepare-and-measure experiments that is neutral with respect to the direction of inference, such that both the retrodictive formalism and the more usual predictive formalism are consequences of a more fundamental description in terms of a conditionally independent tripartite state, and the two formalisms are related by a quantum generalization of Bayes' rule. As an application, a new argument for the compatibility condition for quantum states proposed by Brun, Finklestein and Mermin is given that would be acceptable to a subjective Bayesian.