A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Abstract

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.

Network mechanism for generating genuinely correlative Gaussian states*

“…encode the intermodal correlations between subsystems A i and A j . For any [38,42,43]. It is evident that, for any 2-partition  of n-mode system A 1 A 2 KA n , there exists a permutation π of (1, 2, Kn) and positive integers n 1 , n 2 with…”

“…In fact,  has the following properties which satisfy the basics of Gaussian quantum correlation measure [38,40,[42][43][44][45].…”

Experimental verification of the Gaussian quantum correlation measure in continuous variable systems

“…det(𝜎 𝐴𝐵 ) represents the determinant of the matrix 𝜎 𝐴𝐵 . It is obvious that the Gaussian quantum correlation measure 𝑀 is obtained once we know the elements of the CM, which is much easier to calculate compared with the Gaussian quantum discord [6] . be reconstructed based on the measured data [17] .…”

“…Most of them can only be calculated for (1 + 1)-mode Gaussian states or some special (n + m)-mode Gaussian states. This is mainly because all quantifications of the correlation involve measurements performed on one subsystem and the optimization process, which made them difficult to evaluate [6] .…”

“…Recently, a computable Gaussian quantum correlation measure 𝑀 is proposed [6] . It has some attractive properties such as: 𝑀 is independent of the mean of states, it is symmetric about the subsystems, it has no ancilla problem, and it is locally Gaussian unitary invariant.…”