In this paper, a computable multipartite multimode Gaussian quantum correlation measure ${\mathcal M}^{(k)}$ is proposed for any $k$ -partite continuous-variable (CV) systems with $k\geq 2$ . ${\mathcal M}^{(k)}$ 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 $ρ$ , ${\mathcal M}^{(k)}(ρ)=0$ if and only if $ρ$ is a $k$ -partite product state. Thus, for the bipartite case, ${\mathcal M}={\mathcal M}^{(2)}$ is an accessible replacement of the Gaussian quantum discord and Gaussian geometric discord. Moreover, ${\mathcal M}^{(k)}$ satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey. ${\mathcal M}^{(k)}$ is not bipartite like monogamous, but, ${\mathcal M}^{(k)}$ is complete monogamous and tight complete monogamous.In this paper, a computable multipartite multimode Gaussian quantum correlation measure ${\mathcal M}^{(k)}$ is proposed for any $k$-partite continuous-variable (CV) systems with $k\geq 2$. ${\mathcal M}^{(k)}$ 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 $ρ$, ${\mathcal M}^{(k)}(ρ)=0$ if and only if $ρ$ is a $k$-partite product state. Thus, for the bipartite case, ${\mathcal M}={\mathcal M}^{(2)}$ is an accessible replacement of the Gaussian quantum discord and Gaussian geometric discord. Moreover, ${\mathcal M}^{(k)}$ satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey. ${\mathcal M}^{(k)}$ is not bipartite like monogamous, but, ${\mathcal M}^{(k)}$ is complete monogamous and tight complete monogamous.

arXiv:2001.01244Jan 5, 20200 citations

In this paper, a computable multipartite multimode Gaussian quantum correlation measure

{\mathcal M}^{(k)}

is proposed for any

k

-partite continuous-variable (CV) systems with

k\geq 2

{\mathcal 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

{\mathcal M}^{(k)}(ρ)=0

if and only if

ρ

is a

k

-partite product state. Thus, for the bipartite case,

{\mathcal M}={\mathcal M}^{(2)}

is an accessible replacement of the Gaussian quantum discord and Gaussian geometric discord. Moreover,

{\mathcal M}^{(k)}

satisfies the unification condition, hierarchy condition that a multipartite quantum correlation measure should obey.

{\mathcal M}^{(k)}

is not bipartite like monogamous, but,

{\mathcal M}^{(k)}

is complete monogamous and tight complete monogamous.