Correlation evolution and monogamy of two geometric quantum discords in multipartite systems

TL;DR

This paper investigates two types of geometric quantum discords in multipartite systems, revealing their hierarchy, relation to entanglement, and differing dynamical behaviors, including sudden changes and monogamy properties.

Contribution

It introduces a detailed comparison of GQD-1 and GQD-2, establishing hierarchy relations, their connection to entanglement, and analyzing their dynamical evolution and monogamy in multipartite systems.

Findings

Hierarchy relation between GQD-1 and GQD-2 in symmetric states.

GQD-2 shows sudden change behaviors, GQD-1 evolves asymptotically.

Different monogamous properties of the two GQDs.

Abstract

We explore two different geometric quantum discords defined respectively via the trace norm (GQD-1) and Hilbert-Schmidt norm (GQD-2) in multipartite systems. A rigorous hierarchy relation is revealed for the two GQDs in a class of symmetric two-qubit $X$-shape states. For multiqubit pure states, it is found that both GQDs are related to the entanglement concurrence, with the hierarchy relation being saturated. Furthermore, we look into a four-partite dynamical system consisting of two cavities interacting with independent reservoirs. It is found that the GQD-2 can exhibit various sudden change behaviours, while the GQD-1 only evolves asymptotically, with the two GQDs exhibiting different monogamous properties.