Multipartite generalization of geometric measure of discord

Abstract

Radhakrishnan et al. (2020) proposed a generalization of quantum discord to multipartite systems, which is consistent with the conventional definition of discord in bipartite systems, and derived explicit formulae for any multipartite state. These results are significant in capturing quantum correlations for multi-qubit systems. We propose a generalization of the geometric measure of bipartite quantum discord to the multipartite case in the same manner. We find generic forms of the generalization of the geometric measure of quantum discord in a general N-partite quantum state. Further, we obtain computable exact formulas for the generalization of the geometric measure of quantum discord in an N-qubit quantum state, which includes the results obtained in [arXiv:2104.12344].