On Ruelle transfer operators and completely positive maps

TL;DR

This paper explores the application of Ruelle transfer operators to quantum information theory, establishing links between fixed points of completely positive maps and invariant measures, and analyzing entropy and decay properties.

Contribution

It introduces a novel connection between transfer operators and CPT maps, defining entropy and demonstrating exponential decay in mixed-unitary channels.

Findings

Fixed points of CPT maps correspond to Markov-invariant measures

A new entropy definition induced by transfer operators

Exponential decay property for mixed-unitary channels

Abstract

We consider applications of transfer operators (also known as Ruelle operators) to completely positive maps (CPT) in quantum information theory. It is described a correspondence between fixed points of CPT maps and certain Markov-invariant measures. We also obtain a definition of entropy induced by transfer operators and an exponential decay property for mixed-unitary channels.