Fidelity-based unitary operation-induced quantum correlation for continuous-variable systems

Abstract

We propose a measure of nonclassical correlation N G F in terms of local Gaussian unitary operations based on square of the fidelity F for bipartite continuous-variable systems. This quantity is easier to calculate or estimate and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of N G F for any (1+1)-mode Gaussian states is presented and an estimation of N G F for any (n + m)-mode Gaussian states is given. For any (1 + 1)-mode Gaussian states, N G F does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing N G F (ρ AB ) in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that N G F is much better in detecting quantum correlations of Gaussian states.

A computable multipartite multimode Gaussian correlation measure and the monogamy relation for continuous-variable systems

“…As 1 is a sharp upper bound of N G,A F (Ref. [21]), we see that the upper bound 1 of M is also sharp.…”

“…Inspired by our former work [21], in this paper, we propose a quantum non-locality M for continuousvariable systems in terms of the CM for bipartite multimode states, i.e., (n + m)-mode states. Let SS(H) the set of CV states with finite first and second moments.…”

“…where the supremum is taken over all Gaussian unitary operators U ∈ B(H A ) satisfying U ρ A U † = ρ A with ρ A = Trρ AB the reduced state. By [21,Theorem 5],…”

“…As discussed above, M is a Gaussian correlation measure describes the Gaussian non-product correlation in bipartite continuous-variant systems. Therefore, when restricted to Gaussian states, M describes the same Gaussian non-classicality -a Gaussian state ρ AB is correlated if and only if it is not a product state -as that described by Gaussian QD D [12,13], Gaussian geometric discord D G [14], the correlations Q, Q P proposed in [24], the correlation N F in [20], the correlation N F discussed in [21], and the Gaussian response of discord GD x R (ρ AB ) in [20,22], since they take value 0 at a Gaussian state ρ AB if and only if ρ AB is a product state. Because M is independent of the measurements on a subsystem and the optimization process, unlike those known quantum non-locality, evaluating M will consume less resource.…”

“…Gaussian discriminating strength based on the minimum or maximum change induced on the state by a local action, in the form of a local Gaussian unitary operation were studied in [17][18][19]. Based Gaussian unitary operation and fidelity, several kinds of Gaussian response of discord (GD x R , N F , N F ) were proposed and discussed in [20][21][22]. For other related results, see [23][24][25][26] and the references therein.…”