Irreducible Multiparty Correlations in Quantum States without Maximal Rank

Abstract

The correlations of an n-partite quantum state are classified into a series of irreducible k-party ones (2<or=k<or=n), with the irreducible k-party correlation being the correlation in the states of k parties but nonexistent in the states of (k-1) parties. A measure of the degree of irreducible k-party correlation is defined based on the principle of maximal entropy. Adopting a continuity approach, we overcome the difficulties in calculating the degrees of irreducible multiparty correlations for the multipartite states without maximal rank. In particular, we obtain the degrees of irreducible multiparty correlations in the n-qubit stabilizer states and the n-qubit generalized Greenberger-Horne-Zeilinger states, which reveals the distribution of multiparty correlations.