{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:22:50Z","timestamp":1760242970424,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,12]],"date-time":"2015-03-12T00:00:00Z","timestamp":1426118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004442","name":"National Science Centre","doi-asserted-by":"publisher","award":["DEC-2011\/01\/B\/ST1\/03994"],"award-info":[{"award-number":["DEC-2011\/01\/B\/ST1\/03994"]}],"id":[{"id":"10.13039\/501100004442","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A notion of entropy of a normal state on a finite von Neumann algebra in Segal\u2019s sense is considered, and its superadditivity is proven together with a necessary and sufficient condition for its additivity. Bounds on the entropy of the state after measurement are obtained, and it is shown that a weakly repeatable measurement gives minimal entropy and that a minimal state entropy measurement satisfying some natural additional conditions is repeatable.<\/jats:p>","DOI":"10.3390\/e17031181","type":"journal-article","created":{"date-parts":[[2015,3,12]],"date-time":"2015-03-12T11:30:24Z","timestamp":1426159824000},"page":"1181-1196","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Entropy of Quantum Measurement"],"prefix":"10.3390","volume":"17","author":[{"given":"Hanna","family":"Pods\u0229dkowska","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Sciences, University of \u0141\u00f3d\u017a, ul. S. Banacha 22, 90-238 \u0141\u00f3d\u017a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,12]]},"reference":[{"key":"ref_1","unstructured":"Von Neumann, J. (1955). Mathematische Grundlagen der Quantenmechanik (Mathematical Foundations of Quantum Mechanics), Princeton University Press."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bratteli, O., and Robinson, D.W. (1979). Operator Algebras and Quantum Statistical Mechanics, Springer.","DOI":"10.1007\/978-3-662-02313-6"},{"key":"ref_3","unstructured":"Emch, G.G. (1972). Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Haag, R. (1992). Local Quantum Physics. Fields, Particles, Algebras, Springer.","DOI":"10.1007\/978-3-642-97306-2"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1063\/1.1704187","article-title":"An algebraic approach to quantum field theory","volume":"5","author":"Haag","year":"1964","journal-title":"J. Math. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"930","DOI":"10.2307\/1969387","article-title":"Postulates for general quantum mechanics","volume":"48","author":"Segal","year":"1947","journal-title":"Ann. Math."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Neshveyev, S., and St\u00f8rmer, E. (2006). Dynamical Entropy in Operator Algebras, Springer.","DOI":"10.1007\/3-540-34673-2"},{"key":"ref_8","unstructured":"Petz, D., and Ohya, M. (2004). Quantum Entropy and Its Use, Springer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.3390\/e12051194","article-title":"Quantum entropy and its applications to quantum communication and statistical physics","volume":"12","author":"Ohya","year":"2010","journal-title":"Entropy"},{"key":"ref_10","unstructured":"R\u00f8rdam, M., and St\u00f8rmer, E. (2002). Encyclopaedia of Mathematical Sciences, Springer."},{"key":"ref_11","unstructured":"Davies, E.B. (1976). Quantum Theory of Open Systems, Academic Press."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/BF01647093","article-title":"An operational approach to quantum probability","volume":"18","author":"Davies","year":"1970","journal-title":"Comm. Math. Phys."},{"key":"ref_13","first-page":"623","article-title":"A note on the concept of entropy","volume":"9","author":"Segal","year":"1960","journal-title":"J. Math. Mech."},{"key":"ref_14","first-page":"59","article-title":"Conditional expectation in an operator algebra, IV (Entropy and information)","volume":"14","author":"Umegaki","year":"1962","journal-title":"K\u014ddai Math. Sem. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Busch, P., Lathi, P.J., and Mittelstaedt, P. (1991). The Quantum Theory of Measurement, Springer.","DOI":"10.1007\/978-3-662-13844-1"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"\u0141uczak, A., and Podse\u00b8dkowska, H. (2015). L\u00fcders instruments, generalized L\u00fcders theorem, and some aspects of sufficiency. Int. J. Theor. Phys.","DOI":"10.1007\/s10773-014-2485-y"},{"key":"ref_17","unstructured":"\u0141uczak, A. (1993, January 7\u201310). Characterization of von Neumann instruments in a theory of quantum measurement, Toru\u0144, Poland."},{"key":"ref_18","first-page":"322","article-title":"\u00dcber die Zustands\u00e4nderung durch den Messprozess","volume":"8","year":"1951","journal-title":"Ann. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5872","DOI":"10.1063\/1.1519669","article-title":"Fixed points of quantum operations","volume":"43","author":"Arias","year":"2002","journal-title":"J. Math. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/S0375-9601(98)00704-X","article-title":"L\u00fcders theorem for unsharp quantum measurements","volume":"249","author":"Busch","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, W., and Wunde, J. (2010). Fixed points of commutative L\u00fcders operations. J. Phys. A Math. Theor., 43.","DOI":"10.1088\/1751-8113\/43\/39\/395206"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1023\/A:1009618508213","article-title":"On ideal measurements and their corresponding instruments on von Neumann algebras","volume":"6","year":"1999","journal-title":"Open Syst. Inf. 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