Shannon theory beyond quantum: information content of a source

TL;DR

This paper generalizes the concept of information content from classical and quantum sources to operational probabilistic theories, establishing foundational properties and relations with entropy measures.

Contribution

It extends the definition of information content to operational probabilistic theories and proves key properties and relations with entropy.

Findings

Proves subadditivity of information content in probabilistic theories

Establishes the relation between purity and information content

Provides bounds relating information content to accessible information

Abstract

The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits replacing bits. In the mentioned cases the information content can be quantified through Shannon's and von Neumann's entropy, respectively. Here we extend the definition of information content to operational probabilistic theories, and prove relevant properties as the subadditivity, and the relation between purity and information content of a state. We prove the consistency of the present notion of information content when applied to the classical and the quantum case. Finally, the relation with one of the notions of entropy that can be introduced in general probabilistic theories, the maximum accessible information, is given in terms of a lower bound.