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A Bell inequality which has a larger signal to noise ratio than Clauser-Horne-Shimony-Holt inequality and which can be used to test locality more simply than Clauser-Horne inequality

M. Ardehali

Published May 12, 1998• 0 citations
OpenAlex

Abstract

A Bell inequality is derived from locality and a supplementary assumption. This inequality requires the measurements of only two detection probabilities and has a larger signal to noise ratio than Clauser-Horne-Shimony-Holt inequality.

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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 correlation inequality is derived from local realism and a supplementary assumption. This inequality is violated by a factor of 1.5 in the case of real experiments, whereas previous inequalities such as Clauser-Horne-Shimony-Holt inequality of 1969 and Clauser-Horne inequality of 1974 are violated by a factor of 2\sqrt 22​. Thus the magnitude of violation of this inequality is approximately 20.7% larger than the magnitude of violation of previous inequalities. Moreover, the present inequality can be used to test locality very simply because it requires the measurements of only two detection probabilities. In contrast, Clauser-Horne inequality requires the measurements of five detection probabilities.
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.
We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.
Einstein's locality is invoked to derive a correlation inequality. In the case of ideal experiments, this inequality is equivalent to Bell's original inequality of 1965 which, as is well known, is violated by a maximum factor of 1.5. The crucial point is that even in the case of real experiments where polarizers and detectors are non-ideal, the present inequality is violated by a factor of 1.5, whereas previous inequalities such as Clauser-Horne-Shimony-Holt inequality of 1969 and Clauser-Horne inequality of 1974 are violated by a factor of 2\sqrt 22​. The larger magnitude of violation can be of importance for the experimental test of locality. Moreover, the supplementary assumption used to derive this inequality is weaker than Garuccio-Rapisarda assumption. Thus an experiment based on this inequality refutes a larger family of hidden variable theories than an experiment based on Garuccio-Rapisarda inequality.