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arXiv:quant-ph/9704032 · Physical Review A

Equivalence between Bell’s inequality and a constraint on stochastic field theories for Einstein-Podolsky-Rosen states

Lars M. Johansen

Published Jul 1, 1997• 1 citation
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Abstract

A generalized form of the Einstein Podolsky-Rosen state is defined, embracing both classical and nonclassical states. It is shown that for such states, Bell's inequality is equivalent to a constraint on stochastic field theories. Thus violation of Bell's inequality can be observed also for weak violation of stochastic field theories. The Schr\"odinger-cat state is shown to be an example of this.

DOI
10.1103/physreva.56.100

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A generalized form of the Einstein Podolsky-Rosen state is defined, embracing both classical and nonclassical states. It is shown that for such states, Bell's inequality is equivalent to a constraint on stochastic field theories. Thus violation of Bell's inequality can be observed also for weak violation of stochastic field theories. The Schr"odinger-cat state is shown to be an example of this.
Using homodyning with weak coherent fields and photon counting, we have observed violations of Bell-type inequalities by the generalized Einstein-Podolsky-Rosen state produced in a pulsed nondegenerate optical parametric amplifier, as predicted by Grangier et al. [Phys. Rev. A 38, 3132 (1988)]. The maximum observed visibility of the interference pattern was (89+/-4)%. This interference can be regarded as a manifestation of nonlocality in the sense described by Banaszek and Wodkiewicz [Phys. Rev. A 58, 4345 (1998)]. We have investigated the interference both theoretically and experimentally and have measured the influence of dispersion and phase matching.
Cooperative multiparticle quantum states in an Einstein-Podolsky-Rosen type of experiment are shown to violate a Bell inequality. Thus correlations can occur between wave packets each having NNN bosons which cannot be explained within local hidden-variable theories. This provides a way to test quantum measurement theory for multiparticle states. In these states, a local, positive probability distribution exists for all NNN. However, the representation of correlations with this probability distribution is different from that in standard (Bell-type) hidden-variable theories.
The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin 1/2 particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all hidden variables theories with that kind of nonlocality. In particular, real analyticity leads to negative definite correlations, in contradiction with quantum mechanics.