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 $(\zeta )$. Maximal violation occurs at $\zeta \to \infty$ when the parity of either component averages to zero. For a given entangled {\it 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. {\bf68}, 3259 (1992)). We show that for finite $\zeta$ 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 $\zeta .$ The configurational parameter variation is used to show that BIQV relation to entanglement is, even for pure state, not monotonic.

An example added; shows that the amount of Bell's inequality violation as a measure of entanglement is doubtful

References in corpus (3)

• Direct Probing of Quantum Phase Space by Photon Counting
• Quantum Nonlocality in Phase Space
• Maximal Violation of Bell's Inequalities for Continuous Variable Systems

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