{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:49:29Z","timestamp":1768740569546,"version":"3.49.0"},"reference-count":60,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:00:00Z","timestamp":1717113600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003827","name":"National Research, Development and Innovation Office, Hungary","doi-asserted-by":"publisher","award":["KKP133827"],"award-info":[{"award-number":["KKP133827"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003827","name":"National Research, Development and Innovation Office, Hungary","doi-asserted-by":"publisher","award":["TKP2021-NVA-04"],"award-info":[{"award-number":["TKP2021-NVA-04"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003827","name":"National Research, Development and Innovation Office, Hungary","doi-asserted-by":"publisher","award":["TKP2021-EGA-17"],"award-info":[{"award-number":["TKP2021-EGA-17"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1\/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1\/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.<\/jats:p>","DOI":"10.3390\/e26060485","type":"journal-article","created":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T11:43:48Z","timestamp":1717155828000},"page":"485","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5491-8915","authenticated-orcid":false,"given":"Matyas","family":"Mechler","sequence":"first","affiliation":[{"name":"Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary"},{"name":"Institute of Physics, University of P\u00e9cs, Ifj\u00fas\u00e1g \u00datja 6, H-7624 P\u00e9cs, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1282-4560","authenticated-orcid":false,"given":"Margarita A.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3972-0227","authenticated-orcid":false,"given":"Vladimir I.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0660-9549","authenticated-orcid":false,"given":"Peter","family":"Adam","sequence":"additional","affiliation":[{"name":"Institute for Solid State Physics and Optics, HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary"},{"name":"Institute of Physics, University of P\u00e9cs, Ifj\u00fas\u00e1g \u00datja 6, H-7624 P\u00e9cs, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0375-9601(96)00107-7","article-title":"Symplectic tomography as classical approach to quantum systems","volume":"213","author":"Mancini","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/S0375-9601(97)00199-0","article-title":"Positive distribution description for spin states","volume":"229","author":"Dodonov","year":"1997","journal-title":"Phys. Lett. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1134\/1.558326","article-title":"Spin state tomography","volume":"85","year":"1997","journal-title":"J. Exp. Theor. Phys."},{"key":"ref_4","unstructured":"Man\u2019ko, O. (1998). 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