Information Flow in Non-Unitary Quantum Cellular Automata

TL;DR

This paper introduces a new measure called the information current to quantify information flow in non-unitary quantum cellular automata, extending the existing index theory to open quantum systems with environment coupling.

Contribution

It proposes a novel, locally computable measure of information flow for non-unitary QCA, addressing the limitations of previous index-based methods.

Findings

The information current can be computed locally from matrix-product operator representations.

The measure extends the analysis of information flow to open quantum systems.

It provides a tool for studying non-unitary quantum dynamics in cellular automata.

Abstract

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has been proposed for the quantification of the net flow of quantum information across a boundary. While the index is rigid in the sense of begin invariant under finite-depth local circuits, it is not defined when the system is coupled to an environment, i.e. for non-unitary time evolution of open quantum systems. We propose a new measure of information flow for non-unitary QCA denoted the information current which is not rigid, but can be computed locally based on the matrix-product operator representation of the map.