Entropies in General Probabilistic Theories and its Application to Holevo Bound

TL;DR

This paper introduces a systematic way to construct generalized entropies within general probabilistic theories, extending classical and quantum entropies, and applies these to generalize the Holevo bound across all such theories.

Contribution

It presents a novel systematic method for constructing entropies in general probabilistic theories and extends the Holevo bound to these broad frameworks.

Findings

Generalized entropies encompass Shannon and von Neumann entropies.

The Holevo bound is extended to all general probabilistic theories.

Provides a unified framework for entropy and information bounds in diverse theories.

Abstract

General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this letter, we introduce a systematic method to construct a series of entropies, all of which generalize Shannon entropy in classical system and von Neumann entropy in quantum system. Using these entropies, the Holevo bound, an upper bound of the accessible information from a quantum system, is generalized to hold in any general probabilistic theory.