{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T05:06:26Z","timestamp":1761541586400,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T00:00:00Z","timestamp":1610582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We review the method of quantizers and dequantizers to construct an invertible map of the density operators onto functions including probability distributions and discuss in detail examples of qubit and qutrit states. The biphoton states existing in the process of parametric down-conversion are studied in the probability representation of quantum mechanics.<\/jats:p>","DOI":"10.3390\/sym13010131","type":"journal-article","created":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T01:33:29Z","timestamp":1610674409000},"page":"131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Properties of Quantizer and Dequantizer Operators for Qudit States and Parametric Down-Conversion"],"prefix":"10.3390","volume":"13","author":[{"given":"Peter","family":"Adam","sequence":"first","affiliation":[{"name":"Institute for Solid State Physics and Optics, Wigner Research Center for Physics, P.O. Box 49, H-1525 Budapest, Hungary"},{"name":"Institute of Physics, University of P\u00e9cs, Ifj\u00fas\u00e1g \u00fatja 6, H-7624 P\u00e9cs, Hungary"}]},{"given":"Vladimir A.","family":"Andreev","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, 119991 Moscow, Russia"}]},{"given":"Margarita A.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, 119991 Moscow, Russia"}]},{"given":"Vladimir I.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, 119991 Moscow, Russia"},{"name":"Moscow Institute of Physics and Technology, State University, Institutskii Per. 9, Dolgoprudnyi, 141700 Moscow, Russia"},{"name":"Russian Quantum Center, Skolkovo, 143025 Moscow, Russia"},{"name":"Department of Physics, Tomsk State University, Lenin Avenue 36, 634050 Tomsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5491-8915","authenticated-orcid":false,"given":"Matyas","family":"Mechler","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of P\u00e9cs, Ifj\u00fas\u00e1g \u00fatja 6, H-7624 P\u00e9cs, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1002\/andp.19263840404","article-title":"Quantisierung als Eigenwertproblem (Erste Mitteilung)","volume":"384","year":"1926","journal-title":"Ann. 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