Operator fidelity susceptibility, decoherence and quantum criticality

TL;DR

This paper extends quantum fidelity to operators to analyze environment-induced decoherence, revealing critical behavior and providing exact results for decoherence in an Ising model bath.

Contribution

It introduces state-dependent operator fidelity susceptibility and explores its behavior at quantum critical points, with exact finite-temperature decoherence results.

Findings

OFS exhibits nontrivial behavior at critical points

Two distinct contributions to OFS with different physical origins

Exact finite-temperature decoherence results for Ising bath

Abstract

The extension of the notion of quantum fidelity from the state-space level to the operator one can be used to study environment-induced decoherence. state-dependent operator fidelity sucepti- bility (OFS), the leading order term for slightly different operator parameters, is shown to have a nontrivial behavior when the environment is at critical points. Two different contributions to OFS are identified which have distinct physical origins and temporal dependence. Exact results for the finite-temperature decoherence caused by a bath described by the Ising model in transverse field are obtained.