Problem of Existence of Joint Distribution on Quantum Logic
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 <i>s</i>-map, which is a mathe...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/12/1121 |
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| author | Oľga Nánásiová Karla Čipková Michal Zákopčan |
| author_facet | Oľga Nánásiová Karla Čipková Michal Zákopčan |
| author_sort | Oľga Nánásiová |
| collection | DOAJ |
| description | 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 <i>s</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-variate joint distribution is shown in special cases when the quantum logic consists of at most <i>n</i> blocks of Boolean algebras. |
| format | Article |
| id | doaj-art-f1d080deab99478fa25b5d2a6a3e192e |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-f1d080deab99478fa25b5d2a6a3e192e2025-08-20T02:00:27ZengMDPI AGEntropy1099-43002024-12-012612112110.3390/e26121121Problem of Existence of Joint Distribution on Quantum LogicOľga Nánásiová0Karla Čipková1Michal Zákopčan2Faculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 841 04 Bratislava, SlovakiaFaculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 841 04 Bratislava, SlovakiaFaculty of Electrical Engineering and Information Technology, Slovak University of Technology in Bratislava, Ilkovičova 3, 841 04 Bratislava, SlovakiaThis 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 <i>s</i>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-variate joint distribution is shown in special cases when the quantum logic consists of at most <i>n</i> blocks of Boolean algebras.https://www.mdpi.com/1099-4300/26/12/1121generalized probabilityprobability spacemarginal distributionjoint distributionquantum logicnon-compatibility |
| spellingShingle | Oľga Nánásiová Karla Čipková Michal Zákopčan Problem of Existence of Joint Distribution on Quantum Logic Entropy generalized probability probability space marginal distribution joint distribution quantum logic non-compatibility |
| title | Problem of Existence of Joint Distribution on Quantum Logic |
| title_full | Problem of Existence of Joint Distribution on Quantum Logic |
| title_fullStr | Problem of Existence of Joint Distribution on Quantum Logic |
| title_full_unstemmed | Problem of Existence of Joint Distribution on Quantum Logic |
| title_short | Problem of Existence of Joint Distribution on Quantum Logic |
| title_sort | problem of existence of joint distribution on quantum logic |
| topic | generalized probability probability space marginal distribution joint distribution quantum logic non-compatibility |
| url | https://www.mdpi.com/1099-4300/26/12/1121 |
| work_keys_str_mv | AT olgananasiova problemofexistenceofjointdistributiononquantumlogic AT karlacipkova problemofexistenceofjointdistributiononquantumlogic AT michalzakopcan problemofexistenceofjointdistributiononquantumlogic |