Gamma Spaces and Information

TL;DR

This paper explores the application of Segal's Gamma-spaces to classical and quantum information theory, connecting categorical structures with information loss and spectra of gapped systems.

Contribution

It introduces a novel framework linking Gamma-spaces with information theory, extending the information loss functional to probabilistic and quantum settings.

Findings

Extension of information loss functional to probabilistic Gamma-spaces

Construction of spectra for categories of gapped quantum systems

Unification of classical and quantum information within Gamma-space framework

Abstract

We investigate the role of Segal's Gamma-spaces in the context of classical and quantum information, based on categories of finite probabilities with stochastic maps and density matrices with quantum channels. The information loss functional extends to the setting of probabilistic Gamma-spaces considered here. The Segal construction of connective spectra from Gamma-spaces can be used in this setting to obtain spectra associated to certain categories of gapped systems.