{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T06:40:50Z","timestamp":1782715250843,"version":"3.54.5"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T00:00:00Z","timestamp":1733702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Technical Computer Science and Telecommunication discipline in University of Zielona G\u00f3ra","award":["UGB 701\/2024"],"award-info":[{"award-number":["UGB 701\/2024"]}]},{"name":"Military University of Technology","award":["UGB 701\/2024"],"award-info":[{"award-number":["UGB 701\/2024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory. Some of the known (in the finite-dimensional case) basic properties of the introduced unified entropies were extended to this case study. Certain numerical examples for computing the proposed finite- and infinite-dimensional entropies are outlined as well, which allowed us to calculate the entropy values for infinite Hilbert spaces.<\/jats:p>","DOI":"10.3390\/e26121070","type":"journal-article","created":{"date-parts":[[2024,12,9]],"date-time":"2024-12-09T04:01:37Z","timestamp":1733716897000},"page":"1070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Infinite-Dimensional Quantum Entropy: The Unified Entropy Case"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8657-0829","authenticated-orcid":false,"given":"Roman","family":"Gielerak","sequence":"first","affiliation":[{"name":"Institute of Control & Computation Engineering, University of Zielona G\u00f3ra, Licealna 9, 65-417 Zielona G\u00f3ra, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2119-3329","authenticated-orcid":false,"given":"Joanna","family":"Wi\u015bniewska","sequence":"additional","affiliation":[{"name":"Institute of Information Systems, Faculty of Cybernetics, Military University of Technology, Gen. S. Kaliskiego 2, 00-908 Warszaw, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8468-2456","authenticated-orcid":false,"given":"Marek","family":"Sawerwain","sequence":"additional","affiliation":[{"name":"Institute of Control & Computation Engineering, University of Zielona G\u00f3ra, Licealna 9, 65-417 Zielona G\u00f3ra, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,9]]},"reference":[{"key":"ref_1","first-page":"273","article-title":"Thermodynamik quantenmechanischer Gesamtheiten","volume":"1927","author":"Neumann","year":"1927","journal-title":"Nachrichten Von Der Ges. Der Wiss. G\u00f6Ttingen-Math.-Phys. Kl."},{"key":"ref_2","unstructured":"Nielsen, M.A., and Chuang, I.L. (2010). 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