  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.
