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

Computable multipartite multimode Gaussian quantum correlation measure and the monogamy relations for continuous-variable systems

Jinchuan Hou, Liang Liu, Xiaofei Qi

In this paper, definitions of the unification condition, the hierarchy condition, and three kinds of monogamy relations for multipartite quantum correlation measures are given and discussed. A computable multipartite multimode Gaussian quantum correlation measure ${\mathcal{M}}^{(k)}$ is proposed for any $k$ -partite multimode continuous-variable systems with $k\ensuremath{\ge}2$. The value of ${\mathcal{M}}^{(k)}$ only depends on the covariance matrices of continuous-variable states, is invariant under any permutation of subsystems, has no ancilla problem, is nonincreasing under $k$ -partite local Gaussian channels (particularly, invariant under $k$ -partite locally Gaussian unitary operations), and vanishes on $k$ -partite product states. For a $k$ -partite Gaussian state $\ensuremath{\rho}, {\mathcal{M}}^{(k)}(\ensuremath{\rho})=0$ if and only if $\ensuremath{\rho}$ is a $k$ -partite product state. Moreover, ${\mathcal{M}}^{(k)}$ satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that ${\mathcal{M}}^{(k)}$ is not strongly monogamous but completely monogamous and tightly monogamous.In this paper, definitions of the unification condition, the hierarchy condition, and three kinds of monogamy relations for multipartite quantum correlation measures are given and discussed. A computable multipartite multimode Gaussian quantum correlation measure ${\mathcal{M}}^{(k)}$ is proposed for any $k$-partite multimode continuous-variable systems with $k\ensuremath{\ge}2$. The value of ${\mathcal{M}}^{(k)}$ only depends on the covariance matrices of continuous-variable states, is invariant under any permutation of subsystems, has no ancilla problem, is nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite locally Gaussian unitary operations), and vanishes on $k$-partite product states. For a $k$-partite Gaussian state $\ensuremath{\rho}, {\mathcal{M}}^{(k)}(\ensuremath{\rho})=0$ if and only if $\ensuremath{\rho}$ is a $k$-partite product state. Moreover, ${\mathcal{M}}^{(k)}$ satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that ${\mathcal{M}}^{(k)}$ is not strongly monogamous but completely monogamous and tightly monogamous.

Physical Review AMar 14, 20224 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.

{\mathcal{M}}^{(k)}

is proposed for any

k

-partite multimode continuous-variable systems with $k\ensuremath{\ge}2$. The value of

{\mathcal{M}}^{(k)}

only depends on the covariance matrices of continuous-variable states, is invariant under any permutation of subsystems, has no ancilla problem, is nonincreasing under

k

-partite local Gaussian channels (particularly, invariant under

k

-partite locally Gaussian unitary operations), and vanishes on

k

-partite product states. For a

k

-partite Gaussian state $\ensuremath{\rho}, {\mathcal{M}}^{(k)}(\ensuremath{\rho})=0$ if and only if $\ensuremath{\rho}$ is a

k

-partite product state. Moreover,

{\mathcal{M}}^{(k)}

satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that

{\mathcal{M}}^{(k)}

is not strongly monogamous but completely monogamous and tightly monogamous.