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Communications in Theoretical Physics

Hardy's Theorem for n Spin- s Particles in Entanglement

Wu Xiaohua, Zhao Yumin, Hsia Yuanfu

Published Jul 30, 1998• 0 citations
Publisher

Abstract

The Hardy's theorem [Phys. Rev. Lett. 71 (1993) 1665] is extended to n spin-s particles. As expected, the entangled states for these particles also admit a proof of nonlocality without using inequalities.
DOI
10.1088/0253-6102/30/1/17

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We provide a streamlined proof of Hardy's theorem, that almost every entangled state for a pair of quantum particles admits a ``proof of nonlocality'' without inequalities. Moreover, our analysis covers a larger class of observables. Thus we also strengthen Hardy's assertion that the argument fails for maximally entangled states, such as the singlet state. At the same time, we formulate the argument in such a manner that the relations which must be satisfied for local hidden variables are entirely deterministic, making no reference whatsoever to probability, let alone probablistic inequalities.
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In this paper we provide a simple proof of the fact that for a system of two spin-1/2 particles, and for a choice of observables, there is a unique state which shows Hardy-type nonlocality. Moreover, an explicit expression for the probability that an ensemble of particle pairs prepared in such a state exhibits a Hardy-type nonlocality contradiction is given in terms of two independent parameters related to the observables involved. Incidentally, a wrong statement expressed in Mermin's proof of the converse [N.D. Mermin, Am. J. Phys. 62, 880 (1994)] is pointed out.