Optimization of Bell's inequality violation for continuous variable systems

Abstract

Two mode squeezed vacuum states allow Bell's inequality violation (BIQV) for all non-vanishing squeezing parameter (ζ). Maximal violation occurs at ζ → ∞ when the parity of either component averages to zero. For a given entangled two spin system BIQV is optimized via orientations of the operators entering the Bell operator (cf. S. L. Braunstein, A. Mann and M. Revzen: Phys. Rev. Lett. 68, 3259 (1992)). We show that for finite ζ in continuous variable systems (and in general whenever the dimensionality of the subsystems is greater than 2 ) additional parameters are present for optimizing BIQV. Thus the expectation value of the Bell operator depends, in addition to the orientation parameters, on configuration parameters. Optimization of these configurational parameters leads to a unique maximal BIQV that depends only on ζ. The configurational parameter variation is used to show that BIQV relation to entanglement is, even for pure state, not monotonic.

Bitwise Bell-inequality violations for an entangled state involving2Nions

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“…Previous work [14][15][16][17][18][19] has shown that the state ͉NOPA͘ violates instances of the CHSH inequality with the maximum violation being 2 ͱ 2 [14,18,19]. The violations in Ref.…”

De-Gaussification by inconclusive photon subtraction

“…(93) we should choose a specific representation of the pseudospin operators; note that, as pointed out in Refs. [37,38], the violation of Bell inequalities for continuous variable systems depends, besides on the orientational parameters, on the chosen representation, since different S k leads to different expectation values of B PS . Here we consider the pseudospin operators corresponding to the Wigner functions [37] …”

Violation of Bell?s inequality for continuous-variable EPR states

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