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Journal of Physics A Mathematical and General

Uniqueness of Hardy's state for fixed choice of observables

Guruprasad Kar

Published Apr 21, 1997• 4 citations
Publisher

Abstract

For a system of two spin- particles and for given four observables, two for each and non-commuting, there exists a unique state which admits Hardy's non-locality. Hence, no mixture state admits Hardy's non-locality.
DOI
10.1088/0305-4470/30/8/003

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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.
For a system of nnn spin-12\frac{1}{2}21​ particles and for two measurement possibilities for each particle there is always a state showing Hardy's nonlocality. Mixed states of an nnn- (n> 3)(n>~3)(n> 3) particle system can only show Hardy's nonlocality. Product states for any nnn never show nonlocality.
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