We present a theorem that all generalized Greenberger-Horne-Zeilinger states of a three-qubit system violate a Bell inequality in terms of probabilities. All pure entangled states of a three-qubit system are shown to violate a Bell inequality for probabilities; thus, one has Gisin's theorem for three qubits.

Between 1964 and 1990, the notion of nonlocality in Bell’s papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates ‘local causality’) became divo...

Violation of Bell inequalities for beables is well-known to be possible because of what has become known as the “conspiracy” loophole, but this route to a beables model is properly discounted as implausible, essentially because it requires correlations between instrument settings and hidden beables. This paper identifies a further loophole, called here the “correlation” loophole, which is more ...

We will demonstrate in this paper that Bell′s theorem (Bell′s inequality) does not really conflict with quantum mechanics, the controversy between them originates from the different definitions for the expectation value using the probability distribution in Bell′s inequality and the expectation value in quantum mechanics. We can not use quantum mechanical expectation value measured in experimen...

The Hankel transform of an integer sequence (an) is defined as a sequence formed by the determinants of the matrices An, where An is the upper-left submatrix of size n× n of the Hankel matrix A =  a0 a1 a2 a3 · · · a1 a2 a3 a4 · · · a2 a3 a4 a5 · · · .. .. .. .. . . .  . In this talk, methods in deriving the Hankel transform of Bell and other Bell-type numbers will be discussed, particu...

We consider a question in what condition mixed state which can be decomposed different ways cannot described by single set of hidden variables. The is closely related with Bell theorem.

A proof of Bell's theorem without inequalities is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem based on an entangled state of 2n qubits (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for 2n qubits and it is shown that quantum mec...