{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:57Z","timestamp":1760243157379,"version":"build-2065373602"},"reference-count":130,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T00:00:00Z","timestamp":1445990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures.<\/jats:p>","DOI":"10.3390\/e17117349","type":"journal-article","created":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T13:43:01Z","timestamp":1446039781000},"page":"7349-7373","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Quantum Information as a Non-Kolmogorovian Generalization of Shannon\u2019s Theory"],"prefix":"10.3390","volume":"17","author":[{"given":"Federico","family":"Holik","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica La Plata (IFLP), CONICET, 115 y 49, 1900 La Plata, Argentina"},{"name":"Departamento de F\u00edsica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Gustavo","family":"Bosyk","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica La Plata (IFLP), CONICET, 115 y 49, 1900 La Plata, Argentina"},{"name":"Departamento de F\u00edsica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]},{"given":"Guido","family":"Bellomo","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica La Plata (IFLP), CONICET, 115 y 49, 1900 La Plata, Argentina"},{"name":"Departamento de F\u00edsica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina"}],"role":[{"role":"author","vocab":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10701-004-2010-x","article-title":"Quantum mechanics is about quantum information","volume":"35","author":"Bub","year":"2005","journal-title":"Found. 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