dorsal/arxiv
View SchemaKolmogorov and von Mises viewpoints to the Greenburger-Horne-Zeilinger paradox
| Authors | Andrei Khrennikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0006017 |
| URL | https://arxiv.org/abs/quant-ph/0006017 |
Abstract
We present comparative probabilistic analysis of the Greenburger-Horne-Zeilinger paradox in the frameworks of Kolmogorov's (measure-theoretical) and von Mises' (frequency) models of the probability theory. This analysis demonstrated that the GHZ paradox is merely a consequence of the use of Kolmogorov's probabilistic model. By using von Mises' frequency approach we escape the contradiction between the local realism and quantum formalism. The frequency approach implies automatically contextual interpretation of quantum formalism: different collectives induce different probability distributions. On the other hand, the formal use of Kolmogorov's model implies the identification of such distributions with one abstract Kolmogorov measure. In the measure-theoretical approach we can escape the paradox, if we do not suppose that probability distributions corresponding to different settings of measurement devices are equivalent. We discuss the connection between equivalence/singularity dichotomy in measure theory and the existence of compatible and noncompatible observables.
{
"annotation_id": "d0b13f85-b5f4-4831-a83c-d105462c9c2c",
"date_created": "2026-03-02T18:01:38.741000Z",
"date_modified": "2026-03-02T18:01:38.741000Z",
"file_hash": "8e85182ad06b103c293964c29643a4c01ba16914e81c2e3640848ad726692e83",
"private": false,
"record": {
"abstract": "We present comparative probabilistic analysis of the\nGreenburger-Horne-Zeilinger paradox in the frameworks of Kolmogorov\u0027s\n(measure-theoretical) and von Mises\u0027 (frequency) models of the probability\ntheory. This analysis demonstrated that the GHZ paradox is merely a consequence\nof the use of Kolmogorov\u0027s probabilistic model. By using von Mises\u0027 frequency\napproach we escape the contradiction between the local realism and quantum\nformalism. The frequency approach implies automatically contextual\ninterpretation of quantum formalism: different collectives induce different\nprobability distributions. On the other hand, the formal use of Kolmogorov\u0027s\nmodel implies the identification of such distributions with one abstract\nKolmogorov measure. In the measure-theoretical approach we can escape the\nparadox, if we do not suppose that probability distributions corresponding to\ndifferent settings of measurement devices are equivalent. We discuss the\nconnection between equivalence/singularity dichotomy in measure theory and the\nexistence of compatible and noncompatible observables.",
"arxiv_id": "quant-ph/0006017",
"authors": [
"Andrei Khrennikov"
],
"categories": [
"quant-ph"
],
"title": "Kolmogorov and von Mises viewpoints to the Greenburger-Horne-Zeilinger paradox",
"url": "https://arxiv.org/abs/quant-ph/0006017"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c2e75ed3-307e-45ca-9e0f-5df17d7f6d28",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}