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.
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.
Quantum theory (QT) provides statistical predictions for various physical phenomena. To verify these predictions a considerable amount of data has been accumulated in the 'measurements' performed on the ensembles of identically prepared physical systems or in the repeated 'measurements' on some trapped 'individual physical systems'. The outcomes of these measurements are, in general, some numerical time series registered by some macroscopic instruments. The various empirical probability distributions extracted from these time series were shown to be consistent with the probabilistic predictions of QT. More than 70 years ago the claim was made that QT provided the most complete description of 'individual' physical systems and outcomes of the measurements performed on 'individual' physical systems were obtained in an intrinsically random way. Spin polarization correlation experiments (SPCEs), performed to test the validity of Bell inequalities, clearly demonstrated the existence of strong long-range correlations and confirmed that the beams hitting far away detectors somehow preserve the memory of their common source which would be destroyed if the individual counts of far away detectors were purely random. Since the probabilities describe the random experiments and are not the attributes of the 'individual' physical systems, the claim that QT provides a complete description of 'individual' physical systems seems not only unjustified but also misleading and counter productive. In this paper, we point out that we even do not know whether QT is predictably complete because it has not been tested carefully enough. Namely, it was not proven that the time series of existing experimental data did not contain some stochastic fine structures that could have been averaged out by describing them in terms of the empirical probability distributions. In this paper, we advocate various statistical tests that could be used to search for such fine structures in the data and to answer the title question of this paper. In our opinion a proper understanding of the statistical character of QT and of its limitations is crucial in the domains such as quantum optics and quantum information.
In spite of the fact that statistical predictions of quantum theory (QT) can only be tested if large amount of data is available a claim has been made that QT provides the most complete description of an individual physical system. Einstein’s opposition to this claim and the paradox he presented in the article written together with Podolsky and Rosen in 1935 inspired generations of physicists in their quest for better understanding of QT. Seventy years after EPR article it is clear that without deep understanding of the character and limitations of QT one may not hope to find a meaningful unified theory of all physical interactions, manipulate qubits or construct a quantum computer.. In this paper we present shortly the EPR paper, the discussion, which followed it and Bell inequalities (BI). To avoid various paradoxes we advocate purely statistical contextual interpretation (PSC) of QT. According to PSC a state vector is not an attribute of a single electron, photon, trapped ion or quantum dot. A value of an observable assigned to a physical system has only a meaning in a context of a particular physical experiment PSC does not provide any mental space‐time picture of sub phenomena. The EPR paradox is avoided because the reduction of the state vector in the measurement process is a passage from a description of the whole ensemble of the experimental results to a particular sub‐ensemble of these results. We show that the violation of BI is neither a proof of the completeness of QT nor of its non‐locality. Therefore we rephrase the EPR question and ask whether QT is “predictably “complete or in other words does it provide the complete description of experimental data. To test the “predictable completeness” it is not necessary to perform additional experiments it is sufficient to analyze more in detail the existing experimental data by using various non‐parametric purity tests and other specific statistical tools invented to study the fine structure the time‐series.
Three experimental groups succeeded recently to close, at the same time, locality and fair sampling loopholes and confirmed that realism understood as counterfactual definiteness may not be used to explain quantum phenomena. Since there is now a general consensus that Bell inequalities are violated it is important to understand what does it mean and how can we explain the existence of strong correlations between outcomes of distant measurements, predicted by quantum mechanics. Do we have to announce that: Einstein was wrong, Nature is not local and the correlations are produced due to the quantum magic and emerge, somehow, from outside space-time? We reject such conclusions and we show that violations of various inequalities can neither prove completeness of quantum mechanics nor that Nature is not local. We propose simpler contextual explanation of long range correlations predicted by quantum mechanics which reconciles in some sense Bohr with Einstein and we conclude that there is no evidence that Nature plays dice. We argue that to prove predictable completeness of quantum mechanics one has to search for fine structures in experimental data which might have been averaged out in standard statistical analysis and which were not predicted by the theory.
In the debate of the foundations of quantum theory (QM), Bell’s theorem [1] is an important milestone. Based on Einstein’s criticism of completeness [2], Bell formulated an expression for the correlation between distant spin measurements such as described by Bohm [3]. In Bell’s expression, hidden variables to restore locality and causality to the theory (LHV’s) are introduced through a probability (mass) density function and through their influence upon the elementary measurement functions in the two separate wings (denoted by the Aand the B-wing) of the experiment. Many experiments and theoretical developments arose from Bell’s original paper. The most important experiment was performed by Aspect [4]. Aspect’s results were interpreted as a confirmation of the completeness of quantum mechanics. From that point, QM was considered a non-local theory. In a previous paper [5] the present author argued that there was insufficient ground for this conclusion. The author would like to point that merely an appeal to the simplicity and apparent logical truth of Bell’s theorem is advanced to support the exclusive non-locality interpretation. Beyond that, there is no proof that experimental results must exclusively be interpreted in this manner. According to the author the inequalities of Bell were given the status of theorem without sufficient supportive evidence save simplicity. In this paper it will be demonstrated that such a conclusive supportive argument of Bell’s theorem does not exist because an approximate classical model is possible. The principles of the proposed model can also be expressed in numerical terms. This enables numerical simulation of the experiments on a computer. Let us shortly describe a typical idealized Bell experiment. In such an experiment, from a single source, two particles with opposite spin are sent into opposite directions. For instance, we could think of a positron and an electron arising from para-Positronium that are drawn apart by dipole radiation. Subsequently, in the respective wings of the experimental set-up, the spin of the individual particle is measured with a SternGerlach magnet. The measurements are found to be correlated with the, unitary, parameter vectors of the magnets, a = (a1, a2, a3),b = (b1, b2, b3). It is well-known that the QM correlation for singlet state electron and positron is equal to,
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that the theory provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in standard statistical descriptive analysis, were found in the time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR(2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing quantum phenomena in terms of locally defined elements of reality. In a series of recent papers, we have noticed, however, that this conclusion inadvertently, yet crucially, relies on the assumed existence of an absolute frame of reference, with respect to which it would be possible to describe independently of each other the hypothetical elements of reality and the measurement devices that test them. Otherwise, a non-zero geometric phase may appear in the description of the former with respect to a closed sequence of settings of the latter, leading to the violation of the inequality. Following this observation, we discuss an explicit statistical model, which fully reproduces the predictions of Quantum Mechanics for the Bell experiment.