Entanglement and Bell Inequalities
The entangled quantum states play a key role in quantum information. The association of the quantum state vector with each individual physical system in an attributive way is a source of many false paradoxes and inconsistencies. The paradoxes are avoided if the purely statistical interpretation (SI) of the quantum state vector is adopted. According the SI the quantum theory (QT) does not provide any deterministic prediction for any individual experimental result obtained for a free physical system, for a trapped ion or for a quantum dot. In this article it is shown that if the SI is used then, contrary to the general belief, the QT does not predict for the ideal spin singlet state perfect anti-correlation of the coincidence coumts for the distant detectors. Subsequently the various proofs of the Bell's theorem are reanalyzed and in particular the importance and the implications of the use of the unique probability space in these proofs are elucidated. The use of the unique probability space is shown to be equivalent to the use of the joint probability distributions for the non commuting observables. The experimental violation of the Bell's inequalities proves that the naive realistic particle like spatio- temporal description of the various quantum mechanical experiments is impossible. Of course it does not give any argument for the action at the distance and it does not provide the proof of the completeness of the QM. The fact that the quantum state vector is not an attribute of a single quantum system and that the quantum observables are contextual has to be taken properly into account in any implementation of the quantum computing device.