Geometric Discord for Multi-qubit Systems

Abstract

Radhakrishnan et.al [Phys. Rev. Lett. 124, 110401 (2020)] proposed quantum discord to multipartite systems and derived explicit formulae for any states. These results are significant in capturing quantum correlations for multi-qubit systems. In this paper, we propose the geometric measure of multipartite quantum discord and obtain results for a large family of multi-qubit states. Intriguingly, our results demonstrate that for the family of states, multipartite geometric discord decreases exponentially as the number of parties increases while multipartite quantum discord not, therefore, we conclude that multipartite geometric discord could not reflect multipartite quantum discord in all cases. Furthermore, we investigated the dynamic behavior of geometric discord for the family of two-, three-and four-qubit states under phase noise acting on the first qubit. And we discover that sudden change of multipartite geometric discord can appear when phase noise act only on one part of the two-, three-and four-qubit states.

A note on hidden quantum discord in two- and three-qubit systems under local filtering operations

“…Recently, Li et al [23] proved that quantum discord of the above-mentioned quantum states can be divided into three categories based on the conditional measurement [2]. The authors in [24] proposed a geometric measure of multipartite quantum discord and obtained results for (7). Furthermore, Ali in [25] proposed a generalization of geometric measure of multipartite quantum discord in the same manner and found generic forms of the generalization of geometric quantum discord in a general N-partite quantum state.…”