On the Completeness of Quantum Mechanics
  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. 
Marian Kupczynski