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arXiv:2305.11986

Response: Kupczynski Contextual Locally Causal Probabilistic Models are constrained by Bell theorem

Marian Kupczyński

Published May 19, 2023• 0 citations
arXivHTMLPDF

Abstract

In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring instruments and variables describing physical systems, at the moment of their interactions. These setting dependent variables may be correlated, but not necessarily due to spooky influences or superdeterminism. In several Bell Tests, two time series of distant clicks are converted into finite samples containing pairs of non zero outcomes. This data not only violates CHSH inequalities but also nonsignalling. Our model allows explaining both the raw and the final data in these experiments. Moreover, our model, does not compromise experimenters freedom of choice. The violation of nonsignaling is neither consistent with quantum description of an ideal EPRB experiment nor with standard local realistic and stochastic hidden variable models, thus the title of this article and its conclusion: Kupczynski escape route for local realism is not available are misleading.

DOI
10.48550/arxiv.2305.11986

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In a recent preprint Gill and Lambare, criticize our paper published in Frontiers in Physics. Their criticism is unfounded and misleading. They define a probabilistic coupling, in which BI-CHSH hold for all finite samples. It does not mean, that BI-CHSH hold in our model, in which four incompatible experiments are described by setting dependent random variables implemented on 4 disjoint dedicated probability spaces. A joint probability distribution of these random variables does not exist and may not be used to derive inequalities. Moreover, their probabilistic coupling is useless, for a subsequent contextual model, which we construct to describe final data from Bell tests and to explain, in a locally causal way, the reported violations of inequalities and apparent violations of no-signaling. Neither quantum probabilistic model of an ideal EPRB experiment nor local realistic and stochastic hidden variable models may explain reported non-signaling Therefore; it is obvious that our model extends the set of probability distributions of possible measurements allowed in the standard hidden variable models. Gill and Lambare seem not understand , the main message of our paper, that the violation of BI-CHSH and Eberhard inequalities by finite samples in Bell Tests, no matter how well these tests are designed and performed, does not allow for doubt regarding the existence of objective external physical reality and causal locality in Nature. Our contextual model does not want to circumvent Bell Theorem. Therefore the title of Gill and Lambare paper and the conclusion: Kupczynski's escape route for local realism is not available are misleading and have nothing to do with the content and conclusions of our paper.

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In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring instruments and variables describing physical systems, at the moment of their interactions. These setting dependent variables may be correlated, but not necessarily due to spooky influences or superdeterminism. In several Bell Tests, two time series of distant clicks are converted into finite samples containing pairs of non zero outcomes. This data not only violates CHSH inequalities but also nonsignalling. Our model allows explaining both the raw and the final data in these experiments. Moreover, our model, does not compromise experimenters freedom of choice. The violation of nonsignaling is neither consistent with quantum description of an ideal EPRB experiment nor with standard local realistic and stochastic hidden variable models, thus the title of this article and its conclusion: Kupczynski escape route for local realism is not available are misleading.
In a sequence of papers, Marian Kupczynski has argued that Bell’s theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Despite first appearances, Kupczynksi’s concept of a contextual locally causal probabilistic model is mathematically a special case of a Bell local hidden variables model. Thus, even if one takes account of contextuality in the way he suggests, the Bell–CHSH inequality can still be derived. Violation thereof by quantum mechanics cannot be easily explained away: quantum mechanics and local realism (including Kupczynski’s claimed enlargement of the concept) are not compatible with one another. Further inspection shows that Kupczynski is actually falling back on the detection loophole. Since 2015, numerous loophole-free experiments have been performed, in which the Bell–CHSH inequality is violated, so, despite any other possible imperfections of such experiments, Kupczynski’s escape route for local realism is not available.
In a recent preprint Gill and Lambare, criticize our paper published in Frontiers in Physics. Their criticism is unfounded and misleading. They define a probabilistic coupling, in which BI-CHSH hold for all finite samples. It does not mean, that BI-CHSH hold in our model, in which four incompatible experiments are described by setting dependent random variables implemented on 4 disjoint dedicated probability spaces. A joint probability distribution of these random variables does not exist and may not be used to derive inequalities. Moreover, their probabilistic coupling is useless, for a subsequent contextual model, which we construct to describe final data from Bell tests and to explain, in a locally causal way, the reported violations of inequalities and apparent violations of no-signaling. Neither quantum probabilistic model of an ideal EPRB experiment nor local realistic and stochastic hidden variable models may explain reported non-signaling Therefore; it is obvious that our model extends the set of probability distributions of possible measurements allowed in the standard hidden variable models. Gill and Lambare seem not understand , the main message of our paper, that the violation of BI-CHSH and Eberhard inequalities by finite samples in Bell Tests, no matter how well these tests are designed and performed, does not allow for doubt regarding the existence of objective external physical reality and causal locality in Nature. Our contextual model does not want to circumvent Bell Theorem. Therefore the title of Gill and Lambare paper and the conclusion: Kupczynski's escape route for local realism is not available are misleading and have nothing to do with the content and conclusions of our paper.
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no conspiracy. By imbedding the Bell causal structure in a larger causal network the authors correctly prove, that one can explain and quantify possible violation of measurement independence without evoking the super-determinism. They assume the independence of the variables that causally determine the settings and investigate how they might become correlated with hidden variables. Using their extended causal networks they derive a contextual probabilistic model on which their further correct results are based. The authors seem to ignore that contextual probabilistic model may be derived directly using only probabilistic concepts and incorporating correctly setting dependent variables describing measuring instruments. In these contextual probabilistic models experimenters freedom of choice is not compromised and the results of Bell Tests including an apparent violation of Einsteinian nonsignaling may be explained in a locally causal way. Talking about freedom of choice is misleading and is rooted in incorrect understanding of Bayes Theorem. We explain why freedom of choice should be called noncontextuality and why its violation in Bell Tests confirms only the contextual character of quantum observables. Therefore, contextuality and not experimenters freedom of choice are important resources in quantum information.
A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model (called a violation of measurement independence (MI)) would mean a violation of experimenters’ freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thus they cannot depend on randomly chosen experimental settings. However, if hidden variables describing measuring instruments are correctly incorporated into a contextual probabilistic model a violation of inequalities and an apparent violation of no-signaling reported in Bell tests can be explained without evoking quantum non-locality. Therefore, for us, a violation of Bell-CHSH inequalities proves only that hidden variables have to depend on settings confirming contextual character of quantum observables and an active role played by measuring instruments. Bell thought that he had to choose between non-locality and the violation of experimenters’ freedom of choice. From two bad choices he chose non-locality. Today he would probably choose the violation of MI understood as contextuality.
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.
The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality . In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, consistent with quantum predictions, is possible and it depends explicitly on the context of each experiment. It is also deterministic in the sense that the outcome is determined by supplementary local parameters describing both physical signals and measuring instruments. The existence of such description gives additional arguments that quantum theory is emergent from some more detailed theory respecting causality and local determinism. If quantum theory is emergent then there exist perhaps some fine structures in time-series of experimental data which were not predicted by quantum theory. In this paper we explain how a systematic search for such fine structures can be done. If such reproducible fine structures were found it would show that quantum theory is not predictably complete, which would be a major discovery.