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 -mode continuous-variable system, a computable Gaussian quantum correlation is proposed. For any state of the system, depends only on the covariant matrix of without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, has the following attractive properties: (1) is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) is locally Gaussian unitary invariant; (3) for a Gaussian state , if and only if is a product state; and (4) holds for any Gaussian state and any Gaussian channels and performed on the subsystem A and B, respectively. Therefore, 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 , a noninvasive quantum method for detecting intracellular temperature is proposed.
Highlights
M is independent of the mean of states; M is symmetric about the subsystems: for any state ρ AB via the mutual information I (ρ AB) ∈ F S( H A ⊗ HB ), M( F (ρ AB )) = M(ρ AB ), where F : S( H A ⊗ HB ) → S( HB ⊗ H A ) is the swap defined by
Φ B performed on the subsystem A and B, respectively, we have 0 ≤ M((Φ A ⊗ Φ B )ρ AB ) ≤ M(ρ AB )
All quantifications of Gaussian quantum discord and Gaussian geometric discord for (n + m)-mode bipartite continuous-variable systems have been derived from considering the difference between the Gaussian state and the output after performing some measurements over certain subsystem, and taking an optimization procedure
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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 optimization process, which made them difficult to evaluate. The purpose of this paper is to propose a quantification M for bipartite Gaussian systems in terms of the covariance matrix, which avoids the measurements performed on a subsystem as well as the optimization procedure.
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