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Communications in Theoretical Physics

Optical Test of Local Hidden-Variable Model

Wu Xiao-Hua, Zong Hong-Shi, Pang Hou-Rong

Published Jun 15, 2001• 0 citations
Publisher

Abstract

An inequality is deduced from local realism and a supplementary assumption. This inequality defines an experiment that can be actually performed with the present technology to test local hidden-variable models, and it is violated by quantum mechanics with a factor 1.92, while it can be simplified into a form where just two measurements are required.

DOI
10.1088/0253-6102/35/6/679

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An inequality is deduced from local realism and a supplementary assumption. This inequality defines an experiment that can be actually performed with the present technology to test local hidden-variable models, and it is violated by quantum mechanics with a factor 1.92, while it can be simplified into a form where just two measurements are required.
A correlation inequality is derived from local realism and a supplementary assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt (CHSH) inequality] which is violated by quantum mechanics by a factor of 2\sqrt 22​, this inequality is violated by a factor of 1.5. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, unlike CH (or CHSH) inequality which requires the measurement of five detection probabilities, the present inequality requires the measurement of only two detection probabilities. This inequality can therefore be used to test locality more simply than CH or CHSH inequality.
A local hidden-variable model is exhibited for the experiments by Aspect, Grangier, and Roger [Phys. Rev. Lett. 47, 460 (1981); 49, 91 (1982)] and Aspect, Dalibard, and Roger [Phys. Rev. Lett. 49, 1804 (1982)] measuring polarization correlation of optical-photon pairs. The model agrees with quantum-mechanical predictions for all measurable quantities even with ideal polarizers and detectors, and emphasizes the need of a high degree of directional correlation, besides the correlation of spin (or polarization or other quantities), in any test of locality. It is proved that homogeneous inequalities, involving only coincidence detection rates, cannot discriminate between quantum mechanics and local theories, which invalidates all previously used empirical tests. The role of supplementary assumptions, like the so-called no enhancement, for the derivation of Bell's inequalities is discussed. Finally it is conjectured that quantum mechanics might be compatible with local realism, if we assume that not all self-adjoint operators represent observables and not all density operators represent states.
An inequality is deduced from Einstein's locality and a supplementary assumption. This inequality defines an experiment that can actually be performed with present technology to test local realism. Quantum mechanics violates this inequality a factor of 1.5. In contrast, quantum mechanics violates previous inequalities [for example, those of J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969); S. J. Freedman and I. F. Clauser ibid. 28, 938 (1972); and J. F. Clauser and M. A. Horne, Phys. Rev. D 10, 526 (1974)] by a factor of 2.\sqrt{2}.2​. Thus the magnitude of violation of the inequality derived in this paper is approximately 20.7% larger than the magnitude of violation of previous inequalities. This result can be particularly important for the experimental test of locality.