Marian Kupczynski

Recent experiments allowed concluding that Bell-type inequalities are indeed violated thus it is important to understand what it means and how can we explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that: Einstein was wrong, Nature is nonlocal and nonlocal correlations are produced due to the quantum magic and emerge, somehow, from outside space-time? Fortunately such conclusions are unfounded because if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model then Bell-type inequalities may not be proven .We construct a simple probabilistic model explaining these correlations in a locally causal way. In our model measurement outcomes are neither predetermined nor produced in irreducibly random way. We explain in detail why, contrary to the general belief; an introduction of setting dependent parameters does not restrict experimenters’ freedom of choice. Since the violation of Bell-type inequalities does not allow concluding that Nature is nonlocal and that quantum theory is complete thus the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is not only important for a better understanding of Nature but also for various practical applications of quantum phenomena

Bell-type inequalities are proven using oversimplified probabilistic models and/or counterfactual definiteness (CFD). If setting-dependent variables describing measuring instruments are correctly introduced, none of these inequalities may be proven. In spite of this, a belief in a mysterious quantum nonlocality is not fading. Computer simulations of Bell tests allow people to study the different ways in which the experimental data might have been created. They also allow for the generation of various counterfactual experiments’ outcomes, such as repeated or simultaneous measurements performed in different settings on the same “photon-pair”, and so forth. They allow for the reinforcing or relaxing of CFD compliance and/or for studying the impact of various “photon identification procedures”, mimicking those used in real experiments. Data samples consistent with quantum predictions may be generated by using a specific setting-dependent identification procedure. It reflects the active role of instruments during the measurement process. Each of the setting-dependent data samples are consistent with specific setting-dependent probabilistic models which may not be deduced using non-contextual local realistic or stochastic hidden variables. In this paper, we will be discussing the results of these simulations. Since the data samples are generated in a locally causal way, these simulations provide additional strong arguments for closing the door on quantum nonlocality.

Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioural sciences teach us that random variables ‘measuring’ the same content (the answer to the same Yes or No question) may vary, if ‘measured’ jointly with other random variables. Alice’s and Bob’s raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant ±1 outcomes and to estimate correlations.Marginal expectations, estimated using these final samples, depend on distant settings. Therefore,a system of random variables ‘measured’ in Bell tests is inconsistently connected and it should be analyzed using a Contextuality- by-Default approach, what is done for the first time in this paper.The violation of Bell inequalities and inconsistent connectedness may be explained using a contextual locally causal probabilistic model in which setting dependent variables describing measuring instruments are correctly incorporated. We prove that this model does not restrict experimenters` freedom of choice which is a prerequisite of science. Contextuality seems to be the rule and not an exception; thus, it should be carefully tested.

Bell-CHSH inequalities are trivial algebraic properties satisfied by each line of an Nx4 spreadsheet containing ±1 entries, thus it is surprising that their violation in some experiments allows us to speculate about the existence of non-local influences in nature and casts doubt on the existence of the objective external physical reality. Such speculations are rooted in incorrect interpretations of quantum mechanics and in a failure of local realistic hidden variable models to reproduce quantum predictions for spin polarization correlation experiments (SPCE). In these models, one uses a counterfactual joint probability distribution of only pairwise measurable random variables (A, A′, B, B′) to prove Bell-CHSH inequalities. In SPCE, Alice and Bob, using 4 incompatible pairs of experimental settings, estimate imperfect correlations between clicks registered by their detectors. Clicks announce the detection of photons and are coded by ±1. Expectations of corresponding random variables—E (AB), E (AB′), E (A′B), and E (A′B′)—are estimated and compared with quantum predictions. These estimates significantly violate CHSH inequalities. Since variables (A, A′) and (B, B′) cannot be measured jointly, neither Nx4 spreadsheets nor a joint probability distribution of (A, A′, B, B′) exist, thus Bell-CHSH inequalities may not be derived. Nevertheless, imperfect correlations between clicks in SPCE may be explained in a locally causal way, if contextual setting-dependent parameters describing measuring instruments are correctly included in the description. The violation of Bell-CHSH inequalities may not therefore justify the existence of a spooky action at the distance, super-determinism, or speculations that an electron can be both here and a meter away at the same time. In this paper we review and rephrase several arguments proving that such conclusions are unfounded. Entangled photon pairs cannot be described as pairs of socks nor as pairs of fair dice producing in each trial perfectly correlated outcomes. Thus, the violation of inequalities confirms only that the measurement outcomes and ‘the fate of photons’ are not predetermined before the experiment is done. It does not allow for doubt regarding the objective existence of atoms, electrons, and other invisible elementary particles which are the building blocks of the visible world around us.

Bell-CHSH inequalities are trivial algebraic properties satisfied by each line of an Nx4 spreadsheet containing ±1 entries, thus it is surprising that their violation in some experiments allows us to speculate about the existence of non-local influences in nature and casts doubt on the existence of the objective external physical reality. Such speculations are rooted in incorrect interpretations of quantum mechanics and in a failure of local realistic hidden variable models to reproduce quantum predictions for spin polarization correlation experiments (SPCE). In these models, one uses a counterfactual joint probability distribution of only pairwise measurable random variables (A, A′, B, B′) to prove Bell-CHSH inequalities. In SPCE, Alice and Bob, using 4 incompatible pairs of experimental settings, estimate imperfect correlations between clicks registered by their detectors. Clicks announce the detection of photons and are coded by ±1. Expectations of corresponding random variables—E (AB), E (AB′), E (A′B), and E (A′B′)—are estimated and compared with quantum predictions. These estimates significantly violate CHSH inequalities. Since variables (A, A′) and (B, B′) cannot be measured jointly, neither Nx4 spreadsheets nor a joint probability distribution of (A, A′, B, B′) exist, thus Bell-CHSH inequalities may not be derived. Nevertheless, imperfect correlations between clicks in SPCE may be explained in a locally causal way, if contextual setting-dependent parameters describing measuring instruments are correctly included in the description. The violation of Bell-CHSH inequalities may not therefore justify the existence of a spooky action at the distance, super-determinism, or speculations that an electron can be both here and a meter away at the same time. In this paper we review and rephrase several arguments proving that such conclusions are unfounded. Entangled photon pairs cannot be described as pairs of socks nor as pairs of fair dice producing in each trial perfectly correlated outcomes. Thus, the violation of inequalities confirms only that the measurement outcomes and ‘the fate of photons’ are not predetermined before the experiment is done. It does not allow for doubt regarding the objective existence of atoms, electrons, and other invisible elementary particles which are the building blocks of the visible world around us.

In this paper we give additional arguments in favor of the point of view that the violation of Bell, CHSH and CH inequalities is not due to a mysterious non locality of nature. We concentrate on an intimate relation between a protocol of a random experiment and a probabilistic model which is used to describe it. We discuss in a simple way differences between attributive joint probability distributions and generalized joint probability distributions of outcomes from distant experiments which depend on how the pairing of these outcomes is defined. We analyze in detail experimental protocols implied by local realistic and stochastic hidden variable models and show that they are incompatible with the protocols used in spin polarization correlation experiments. We discuss also the meaning of “free will”, differences between quantum and classical filters, contextuality of Kolmogorov models, contextuality of quantum theory and show how this contextuality has to be taken into account in probabilistic models trying to explain in an intuitive way the predictions of QT. The long range imperfect correlations between the clicks of distant detectors can be explained by partially preserved correlations between the signals created by a source. These correlations can only be preserved if the clicks are produced in a local and deterministic way depending on intrinsic parameters describing signals and measuring devices in the moment of the measurement. If an act of a measurement was irreducibly random they would be destroyed. It seems to indicate that QT may be in fact emerging from some underlying more detailed theory of physical phenomena. If this was a case then there is a chance to find in time series of experimental data some fine structures not predicted by QT. This would be a major discovery because it would not only prove that QT does not provide a complete description of individual physical systems but it would prove that it is not predictably complete

In 1976, I met John Bell several times in CERN and we talked about a possible violation of optical theorem, purity tests, EPR paradox, Bell’s inequalities and their violation. In this review, I resume our discussions, and explain how they were related to my earlier research. I also reproduce handwritten notes, which I gave to Bell during our first meeting and a handwritten letter he sent to me in 1982. We have never met again, but I have continued to discuss BI-CHSH inequalities and their violation in several papers. The research stimulated by Bell’s papers and experiments performed to check his inequalities led to several important applications of quantum entanglement in quantum information and quantum technologies. Unfortunately, it led also to extraordinary metaphysical claims and speculations which in our opinion John Bell would not endorse today. BI-CHSH inequalities are violated in physics and in cognitive science, but it neither proved the completeness of quantum mechanics nor its nonlocality. Quantum computing advantage is not due to some magical instantaneous influences between distant physical systems. Therefore one has to be _cautious in drawing-far-reaching philosophical conclusions from Bell’s inequalities_. The true resource for quantum computing is contextuality and not nonlocality.

Ilya Schmelzer wrote recently: Nieuwenhuizen argued that there exists some “contextuality loophole” in Bell’s theorem. This claim in unjustified. It is made clear that this arose from attaching a meaning to the title and the content of the paper different from the one intended by Nieuwenhuizen. “Contextual loophole” means only that if the supplementary parameters describing measuring instruments are correctly introduced, Bell and Bell-type inequalities may not be proven. It is also stressed that a hidden variable model suffers from a “contextuality loophole” if it tries to describe different sets of incompatible experiments using a unique probability space and a unique joint probability distribution.