To freeze or not to: Quantum correlations under local decoherence

TL;DR

This paper establishes conditions for the freezing of quantum correlations under local noise, introduces a freezing index to quantify this phenomenon, and explores its relation to quantum phase transitions.

Contribution

It provides necessary and sufficient conditions for quantum correlation freezing and introduces a freezing index to quantify and analyze this effect.

Findings

Freezing conditions depend on inhomogeneity of magnetizations.

Frozen quantum correlations follow a complementarity relation.

Freezing index can detect quantum phase transitions.

Abstract

We provide necessary and sufficient conditions for freezing of quantum correlations as measured by quantum discord and quantum work deficit in the case of bipartite as well as multipartite states subjected to local noisy channels. We recognize that inhomogeneity of the magnetizations of the shared quantum states plays an important role in the freezing phenomena. We show that the frozen value of the quantum correlation and the time interval for freezing follow a complementarity relation. For states which do not exhibit "exact" freezing, but can be frozen "effectively", by having a very slow decay rate with suitable tuning of the state parameters, we introduce an index -- the freezing index -- to quantify the goodness of freezing. We find that the freezing index can be used to detect quantum phase transitions and discuss the corresponding scaling behavior.