Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.
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.
A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states.
We propose a measure of nonclassical correlation [Formula: see text] in terms of local Gaussian unitary operations based on square of the fidelity [Formula: see text] for bipartite continuous-variable systems. This quantity is easier to be calculated or estimated and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of [Formula: see text] for any [Formula: see text]-mode Gaussian states is presented and an estimation of [Formula: see text] for any [Formula: see text]-mode Gaussian states is given. For any [Formula: see text]-mode Gaussian states, [Formula: see text] does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing [Formula: see text] in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that [Formula: see text] is much better in detecting quantum correlations of Gaussian states.
In recent years the paradigm based on entanglement as the unique measure of quantum correlations has been challenged by the rise of new correlation concepts, such as quantum discord, able to reveal quantum correlations that are present in separable states. It is in general difficult to compute quantum discord, because it involves a minimization over all possible local measurements in a bipartition. In the realm of continuous-variable (CV) systems, a Gaussian version of quantum discord has been put forward upon restricting to Gaussian measurements. It is natural to ask whether non-Gaussian measurements can lead to a stronger minimization than Gaussian ones. Here we focus on two relevant classes of two-mode Gaussian states: squeezed thermal states and mixed thermal states, and allow for a range of experimentally feasible non-Gaussian measurements, comparing the results with the case of Gaussian measurements. We provide evidence that Gaussian measurements are optimal for Gaussian states.
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
M(k) is proposed for any
k-partite multimode continuous-variable systems with $k\ensuremath{\ge}2$. The value of
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,
M(k) satisfies the unification condition and the hierarchy condition that a multipartite quantum correlation measure should obey. We also show that
M(k) is not strongly monogamous but completely monogamous and tightly monogamous.
We extend the quantum discord to continuous variable systems and evaluate Gaussian quantum discord C(ϱ) for bipartite Gaussian states. In particular, for squeezed-thermal states, we explicitly maximize the extractable information over Gaussian measurements: C(ϱ) is minimized by a generalized measurement rather than a projective one. Almost all squeezed-thermal states have nonzero Gaussian discord: They may be either separable or entangled if the discord is below the threshold C(ϱ) = 1, whereas they are all entangled above the threshold. We elucidate the general role of state parameters in determining the discord and discuss its evolution in noisy channels.