{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:11:25Z","timestamp":1768738285245,"version":"3.49.0"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T00:00:00Z","timestamp":1701820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Russian Science Foundation","award":["19-71-10091"],"award-info":[{"award-number":["19-71-10091"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Jordan\u2013Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1\/2 su(2)-group states) and even and odd Schr\u00f6dinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan\u2013Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.<\/jats:p>","DOI":"10.3390\/e25121628","type":"journal-article","created":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T03:48:41Z","timestamp":1701834521000},"page":"1628","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5489-698X","authenticated-orcid":false,"given":"Julio A.","family":"L\u00f3pez-Sald\u00edvar","sequence":"first","affiliation":[{"name":"Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543, Ciudad de Mexico 04510, Mexico"},{"name":"Department of Theoretical Physics, Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow 141700, Russia"},{"name":"Russian Quantum Center, Skolkovo, Moscow 143025, Russia"},{"name":"Laboratory of Quantum Information Technologies, National University of Science and Technology (MISIS), Moscow 119049, Russia"}]},{"given":"Olga V.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"},{"name":"Special Educational Scientific Center, Bauman Moscow State Technical University, The 2nd Baumanskaya Street 5, Moscow 105005, Russia"}]},{"given":"Margarita A.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"}]},{"given":"Vladimir I.","family":"Man\u2019ko","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow 141700, Russia"},{"name":"Russian Quantum Center, Skolkovo, Moscow 143025, Russia"},{"name":"Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1007\/BF01343064","article-title":"Das D\u00e4mpfungsproblem in der Wellenmechanik","volume":"45","author":"Landau","year":"1927","journal-title":"Z. 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