Quantum Communication and Mixed-State Order in Decohered Symmetry-Protected Topological States

TL;DR

This paper explores how decohered symmetry-protected topological states can still transmit quantum information, identifying new quantum channels that preserve order despite decoherence and analyzing their information transmission capabilities.

Contribution

It introduces symmetry-decoupling channels that maintain quantum order in mixed states and relates their properties to quantum information transmission.

Findings

Decohered SPT states can still be used for quantum communication.

Symmetry-decoupling channels protect quantum order without preserving symmetries.

Quantum information transmission is quantified via coherent quantum information.

Abstract

Certain pure-state symmetry-protected topological orders (SPT) can be used as a resource for transmitting quantum information. Here, we investigate the ability to transmit quantum information using decohered SPT states, and relate this property to the "strange correlation functions" which diagnose quantum many-body orders in these mixed-states. This perspective leads to the identification of a class of quantum channels -- termed symmetry-decoupling channels -- which do not necessarily preserve any weak or strong symmetries of the SPT state, but nevertheless protect quantum many-body order in the decohered mixed-state. We quantify the ability to transmit quantum information in decohered SPT states through the coherent quantum information, whose behavior is generally related to a decoding problem, whereby local measurements in the system are used to attempt to "learn" the symmetry charge of the SPT state before decoherence.