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Entropy
Volume 26
Issue 12
10.3390/e26121121
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Problem of Existence of Joint Distribution on Quantum Logic †

by
Oľga Nánásiová
*,‡,
Karla Čipková
‡ and
Michal Zákopčan
‡
Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 841 04 Bratislava, Slovakia
*
Author to whom correspondence should be addressed.
†
Dedicated to Prof. Jaroslaw Pykacz (deceased in 2021).
‡
These authors contributed equally to this work.
Entropy 2024, 26(12), 1121; https://doi.org/10.3390/e26121121 (registering DOI)
Submission received: 31 October 2024 / Revised: 30 November 2024 / Accepted: 19 December 2024 / Published: 21 December 2024
(This article belongs to the Special Issue Quantum Probability and Randomness V)
Versions Notes

Abstract

This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitable for constructing virtual joint probabilities of even non-compatible propositions. The paper completes conclusions published in 2020 and extends the results for three or more random variables if the marginal distributions are known. The existence of a (n+1)-variate joint distribution is shown in special cases when the quantum logic consists of at most n blocks of Boolean algebras.
Keywords: generalized probability; probability space; marginal distribution; joint distribution; quantum logic; non-compatibility; maps for simultaneous measurements generalized probability; probability space; marginal distribution; joint distribution; quantum logic; non-compatibility; maps for simultaneous measurements

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MDPI and ACS Style

Nánásiová, O.; Čipková, K.; Zákopčan, M. Problem of Existence of Joint Distribution on Quantum Logic. Entropy 2024, 26, 1121. https://doi.org/10.3390/e26121121

AMA Style

Nánásiová O, Čipková K, Zákopčan M. Problem of Existence of Joint Distribution on Quantum Logic. Entropy. 2024; 26(12):1121. https://doi.org/10.3390/e26121121

Chicago/Turabian Style

Nánásiová, Oľga, Karla Čipková, and Michal Zákopčan. 2024. "Problem of Existence of Joint Distribution on Quantum Logic" Entropy 26, no. 12: 1121. https://doi.org/10.3390/e26121121

APA Style

Nánásiová, O., Čipková, K., & Zákopčan, M. (2024). Problem of Existence of Joint Distribution on Quantum Logic. Entropy, 26(12), 1121. https://doi.org/10.3390/e26121121

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