A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

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 [Formula: see text]-mode continuous-variable system, a computable Gaussian quantum correlation [Formula: see text] is proposed. For any state [Formula: see text] of the system, [Formula: see text] depends only on the covariant matrix of [Formula: see text] without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, [Formula: see text] has the following attractive properties: (1) [Formula: see text] is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) [Formula: see text] is locally Gaussian unitary invariant; (3) for a Gaussian state [Formula: see text] , [Formula: see text] if and only if [Formula: see text] is a product state; and (4) [Formula: see text] holds for any Gaussian state [Formula: see text] and any Gaussian channels [Formula: see text] and [Formula: see text] performed on the subsystem A and B, respectively. Therefore, [Formula: see text] 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 [Formula: see text] , a noninvasive quantum method for detecting intracellular temperature is proposed.