Has Bell's inequality a general meaning for hidden-variable theories?

Luis de la Peña, Ana Marı́a Cetto, Thomas A. Brody

Willy De Baere

Miklós Rédei

Tan Tian-rong

It is pointed that Bell had two misunderstandings for his work: Firstly,the hidden variable theory that he applied for deriving Bell's inequality keeps wholly intact the operating rules of classical probabilistic theory,but he regarded it as the general local hidden variable theory.Secondly,in Bell's work,the promise actually deriving Bell's inequality is not the one that Bell regarded as the character of local hidden variable theory.Also,other versions can prove Bell's inequality without local hidden variable theory and the Lochak's objection against Bell's theory are examined.

Bryan J. Dalton

Abstract In this paper we consider the description by a general Bell-type non-local hidden variable theory of bipartite quantum states with two observables per sub-system. We derive Bell inequalities of the Collins-Gisin.-Liden-Massar-Popescu type which involve combinations of the probabilities of related outcomes for measurements for the four pairs of sub-system observables. It is shown that the corresponding quantum theory expressions violate the Bell inequalities in the case of the maximally entangled state of the bipartitite system. The CHSH Bell inequality is also derived from this general CGLMP Bell-type non-local hidden variable theory. This shows that quantum theory can not be underpinned by a Bell-type non-local hidden variable theory. So as a general Bell-type local hidden variable theory has already been shown to conflict with quantum theory, it follows that quantum theory can not be understood in terms of any CGLMP Bell-type hidden variable theory—local or non-local.

Angel G Valdenebro

Several authors have recently claimed that Bell's inequalities (BI) do not apply to certain types of generalized local hidden variables (HV) models. These claims are rejected, by means of a proof of BI valid for a very broad class of local HV models (deterministic or stochastic, with or without memory, time dependent or time independent, setting dependent or setting independent, and even allowing classical communication between the wings of the experiment). The precise meaning of the locality requirement is clarified during the proof. The exact roles of the two assumptions that amount to Bell's locality (parameter independence and outcome independence) are explicitly shown, using each one of them in a different step of the proof. using each one of them in a different step of the proof.