  Quantum cryptography, quantum computer project, space-time quantization
program and recent computer experiments reported by Accardi and his
collaborators show the importance and actuality of the discussion of the
completeness of quantum mechanics (QM) started by Einstein more than 70 years
ago. Many years ago we pointed out that the violation of Bell's inequalities is
neither a proof of completeness of QM nor an indication of the violation of
Einsteinian causality. We also indicated how and in what sense a completeness
of QM might be tested with the help of statistical nonparametric purity tests.
In this paper we review and refine our arguments. We also point out that the
statistical predictions of QM for two-particle correlation experiments do not
give any deterministic prediction for a single pair. After beam is separated we
obtain two beams moving in opposite directions. If the coincidence is reported
it is only after the beams had interacted with corresponding measuring devices
and two particles had been detected. This fact has implications for quantum
cryptography. Namely a series of the measurements performed on the beam by Bob
and converted into a string of bits (secret key) will in general differ, due to
lack of strict anti-correlations, from a secret key found by Alice using the
same procedure.
