Distinguishability Measures and Entropies for General Probabilistic Theories

TL;DR

This paper develops and investigates distinguishability measures and entropies within general probabilistic theories, enabling reformulation of key information-theoretic principles without relying solely on quantum theory.

Contribution

It introduces new distinguishability measures and entropies for general probabilistic theories and applies them to fundamental information-theoretic theorems.

Findings

Reformulation of no-cloning theorems

Reformulation of information-disturbance theorems

Bound on accessible information in general probabilistic theories

Abstract

As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications, no-cloning theorems, information-disturbance theorems are reformulated, and a bound of the accessible informations is discussed in any general probabilistic theories, not resorting to quantum theory.