Proofs of nonlocality without inequalities revisited

G. C. Ghirardi

G. C. Ghirardi, Luca Marinatto

Jose Luis Cereceda

In this paper we extend the ladder proof of nonlocality without inequalities for two spin-half particles given by Boschi et al (Boschi D et al 1997 Phys. Rev. Lett. 79 2755) to the case in which the measurement settings of the apparatus measuring one of the particles are different from the measurement settings of the apparatus measuring the other particle. It is shown that, in any case, the proportion of particle pairs for which the contradiction with local realism goes through is maximized when the measurement settings are the same for each apparatus. Also we write down a Bell inequality for the experiment in question which is violated by quantum mechanics by an amount which is twice as much as the amount by which quantum mechanics violates the Bell inequality considered in the above paper by Boschi et al .

Jaykov Foukzon, Менькова Елена Романовна, Alexander A Potapov

Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.

Peter Rastall

Jose Luis Cereceda

In a recent Brief Report, Zheng [S-B. Zheng, PRA 66, 014103 (2002)] has given a proof of nonlocality without using inequalities for three spin-1/2 particles in the nonmaximally entangled state |psi> = cosθ|+++> + i sinθ|-->. Here we show that Zheng's proof is not correct. Indeed it is the case that, for the experiment considered by Zheng, the only state that admits a nonlocality proof without inequalities is the maximally entangled state.