Reversibility in one-dimensional quantum cellular automata in the presence of noise

TL;DR

This paper explores the reversibility of noisy one-dimensional quantum cellular automata, introducing a method to measure irreversibility and analyzing how noise affects the automaton's dynamics and attractors.

Contribution

It proposes a framework for assessing reversibility in noisy quantum cellular automata by defining an approximate reverse automaton and an irreversibility time based on state distance.

Findings

Irreversibility time is determined by the distance to the maximally mixed state.

Dephasing noise causes the automaton to converge to the maximally mixed state.

An approximate reverse automaton can partially recover the original state in noisy conditions.

Abstract

We consider a class of noisy, one-dimensional quantum cellular automata that allow one to shift from unitary dynamics to completely positive maps, and investigate the notion of reversibility in such a setting. To this aim, we associate an approximate reverse automaton to each noisy automaton, and assess its effect, and we define an irreversibility time based on the distance from the maximally mixed state, which is shown to be the only attractor of the automaton map in the presence of dephasing.