Entanglement and Bell Inequalities

Abstract

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 paradoxes and inconsistencies. The paradoxes are avoided if the purely statistical interpretation (SI) of the quantum state vector is adopted. According to 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 counts 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.

The Contextuality Loophole is Fatal for the Derivation of Bell Inequalities: Reply to a Comment by I. Schmelzer

“…CFD is in conflict with the description of the measurements in quantum theory and with Bohr's complementarity (the measurements of incompatible physical observables represented by non-commuting operators require mutually exclusive experimental contexts) see for example [5][6][7][8][9][10][11] . A detailed discussion why Alice can not predict with certainty Bob's outcome in spin polarization experiments, and vice-versa, may be found for example in [12][13][14] .…”

Time Series, Stochastic Processes and Completeness of Quantum Theory

“…Subtle statistical analysis of the time series of the data using the tools described above and in [21,22] is an appropriate method to test the completeness and the limitations of QT. The statements that the violation of Bell inequalities proves the non locality of QT and/or its completeness are simply not true [2,3,7,9,13,14,16,[23][24][25] and it is really strange how often they have been repeated in the past and even during this conference.…”

“…The arguments in favor of this interpretation and many other references may be found in Balletine [4,5], Accardi [6][7][8], Khrennikov [9][10][11] and in [3,[12][13][14][15][16].…”

EPR Paradox, Locality and Completeness of Quantum Theory

“…by Accardi et al [22,25], Khrennikov [20], Hess and Phillip [24], Kracklauer [28] and by myself. [22,26,27]. We already explained why the formula (6) did not apply to SPCE .…”

“…[20][21][22][23][24][25][26][27][46][47][48][49][50]. Several local models [2,3,28,29,41] were able to reproduce QT predictions.…”