A computable multipartite multimode Gaussian correlation measure and the monogamy relation for continuous-variable systems

Abstract

In this paper, a computable multipartite multimode Gaussian quantum correlation measure M (k) is proposed for any k-partite continuous-variable (CV) systems with k ≥ 2. M (k) depends only on the covariance matrix of CV states, is invariant under any permutation of subsystems, is a quantification without ancilla problem, nonincreasing under k-partite local Gaussian channels (particularly, invariant under k-partite local Gaussian unitary operations), vanishes on k-partite product states. For a k-partite Gaussian state ρ, M (k) (ρ) = 0 if and only if ρ is a k-partite product state. Thus, for the bipartite case, M = M (2) is an accessible replacement of the Gaussian quantum discord and Gaussian geometric discord. Moreover, M (k) satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey. M (k) is not bipartite like monogamous, but, M (k) is complete monogamous and tight complete monogamous.