Abstract
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von Neumann entropy. These quantities allow us to find new proofs of some standard results in quantum information theory, such as the concavity of von Neumann entropy and Holevo’s theorem. The existence of an underlying probability distribution helps shed light on the conceptual underpinnings of these results.
•New forms of quantum conditional entropy and mutual information defined using underlying quantum conditional probability.•New proofs for quantum information theoretic identities.•Additional relationships explored involving system–subsystem relationships.•Generalizations of conditional probabilities discussed.