dorsal/arxiv
View SchemaWigner's inequality for conditional probabilities and nonexistence of a realistic model for the two dimensional Hilbert space
| Authors | Andrei Khrennikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308078 |
| URL | https://arxiv.org/abs/quant-ph/0308078 |
Abstract
We perform the analysis of probabilistic assumptions of Bell's approach. We emphasize that J. Bell wrote about probability without to specify the concrete axiomatics of probability theory. The careful analysis demonstrated that (surprisingly) J. Bell did not apply the classical probability model (Kolmogorov) to describe ``classical physical framework.'' In fact, he created his own probabilistic model and compared it with the quantum one. The crucial point is that J. Bell did not pay attention to {\it conditional probabilities.} We show that conditional probability in his model cannot be defined by classical Bayes' formula. We also use the approach based on Bell-type inequalities in the conventional probabilistic approach, Kolmogorov model. We prove an analog of Wigner's inequality for conditional probabilities and by using this inequality show that predictions of the conventional and quantum probability models disagree already in the case of noncomposite systems (even in the two dimensional case).
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"date_created": "2026-03-02T18:01:59.936000Z",
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"abstract": "We perform the analysis of probabilistic assumptions of Bell\u0027s approach. We\nemphasize that J. Bell wrote about probability without to specify the concrete\naxiomatics of probability theory. The careful analysis demonstrated that\n(surprisingly) J. Bell did not apply the classical probability model\n(Kolmogorov) to describe ``classical physical framework.\u0027\u0027 In fact, he created\nhis own probabilistic model and compared it with the quantum one. The crucial\npoint is that J. Bell did not pay attention to {\\it conditional probabilities.}\nWe show that conditional probability in his model cannot be defined by\nclassical Bayes\u0027 formula. We also use the approach based on Bell-type\ninequalities in the conventional probabilistic approach, Kolmogorov model. We\nprove an analog of Wigner\u0027s inequality for conditional probabilities and by\nusing this inequality show that predictions of the conventional and quantum\nprobability models disagree already in the case of noncomposite systems (even\nin the two dimensional case).",
"arxiv_id": "quant-ph/0308078",
"authors": [
"Andrei Khrennikov"
],
"categories": [
"quant-ph"
],
"title": "Wigner\u0027s inequality for conditional probabilities and nonexistence of a realistic model for the two dimensional Hilbert space",
"url": "https://arxiv.org/abs/quant-ph/0308078"
},
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