Asymptotics of quantum channels

TL;DR

This paper analyzes the long-term behavior of quantum channels, revealing how permutations influence their asymptotic dynamics and providing new theoretical insights into their attractor structures.

Contribution

It introduces an explicit asymptotic map for quantum channels, explores the impact of permutations, and establishes a constructive unfolding theorem for asymptotic dynamics.

Findings

Permutations generally induce non-unitary asymptotic evolution.

The asymptotic map explicitly describes the channel's action on its attractor.

A constructive unfolding theorem for asymptotic dynamics is established.

Abstract

We discuss several aspects concerning the asymptotic dynamics of dicrete-time semigroups associated with a quantum channel. By using an explicit expression of the asymptotic map, which describes the action of the quantum channel on its attractor manifold, we investigate the role of permutations in the asymptotic dynamics. We show that, in general, they make the asymptotic evolution non-unitary, and they are related to the divisibility of the quantum channel. Also, we derive several results about the asymptotics of faithful and non-faithful channels, and we establish a constructive unfolding theorem for the asymptotic dynamics.