One-norm geometric quantum discord under decoherence

TL;DR

This paper analytically studies the behavior of 1-norm geometric quantum discord under decoherence, revealing phenomena like double sudden changes and freezing, contrasting with other norms, with implications for quantum spin chains.

Contribution

It provides the first analytical characterization of 1-norm geometric quantum discord dynamics under decoherence, including conditions for sudden changes and freezing behaviors.

Findings

Double sudden changes can occur in the discord evolution.

Freezing of discord is possible under certain conditions.

Contrasts with Hilbert-Schmidt norm behavior.

Abstract

Geometric quantum discord is a well-defined measure of quantum correlation if Schatten 1-norm (trace norm) is adopted as a distance measure. Here, we analytically investigate the dynamical behavior of the 1-norm geometric quantum discord under the effect of decoherence. By starting from arbitrary Bell-diagonal mixed states under Markovian local noise, we provide the decays of the quantum correlation as a function of the decoherence parameters. In particular, we show that the 1-norm geometric discord exhibits the possibility of double sudden changes and freezing behavior during its evolution. For non-trivial Bell-diagonal states under simple Markovian channels, these are new features that are in contrast with the Schatten 2-norm (Hilbert-Schmidt) geometric discord. The necessary and sufficient conditions for double sudden changes as well as their exact locations in terms of decoherence probabilities are provided. Moreover, we illustrate our results by investigating decoherence in quantum spin chains in the thermodynamic limit.