Quantum Conditional Probabilities and New Measures of Quantum Information

TL;DR

This paper introduces a new quantum conditional probability framework to define novel measures of quantum information, providing fresh insights and proofs for key quantum information theory results.

Contribution

It presents a novel form of quantum conditional probability and new quantum information measures, offering alternative proofs for established theorems and deeper conceptual understanding.

Findings

New quantum information measures related to conditional probability

Alternative proofs of von Neumann entropy concavity and Holevo's theorem

Enhanced conceptual understanding of quantum information theory

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.