General monogamy property of global quantum discord and the application

TL;DR

This paper establishes new monogamy inequalities for global quantum discord, extending existing relations, and applies these to analyze quantum phase transitions in the transverse field Ising model.

Contribution

It introduces a family of generalized monogamy inequalities for GQD and explores their implications and applications in quantum phase transition analysis.

Findings

Monogamy inequalities for GQD are satisfied under specific conditions.

Residual GQD can characterize quantum phase transitions.

New types of monogamy inequalities are proven to hold in certain scenarios.

Abstract

We provide a family of general monogamy inequalities for global quantum discord (GQD), which can be considered as an extension of the usual discord monogamy inequality. It can be shown that those inequalities are satisfied under the similar condition for the holding of usual monogamy relation. We find that there is an intrinsic connection among them. Furthermore, we present a different type of monogamy inequality and prove that it holds under the condition that the bipartite GQDs do not increase when tracing out some subsystems. We also study the residual GQD based on the second type of monogamy inequality. As applications of those quantities, we investigate the GQDs and residual GQD in characterizing the quantum phase transition in the transverse field Ising model.