Entropy of Quantum Measurement
| dc.contributor.author | Podsędkowska, Hanna | |
| dc.date.accessioned | 2015-06-23T10:51:47Z | |
| dc.date.available | 2015-06-23T10:51:47Z | |
| dc.date.issued | 2015-03-12 | |
| dc.identifier.issn | 1099-4300 | |
| dc.identifier.uri | http://hdl.handle.net/11089/10061 | |
| dc.description.abstract | A notion of entropy of a normal state on a finite von Neumann algebra in Segal’s 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. | pl_PL |
| dc.language.iso | en | pl_PL |
| dc.publisher | MDPI | pl_PL |
| dc.relation.ispartofseries | Entropy;2015, 17 | |
| dc.rights | Uznanie autorstwa 3.0 Polska | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/3.0/pl/ | * |
| dc.subject | entropy | pl_PL |
| dc.subject | von Neumann algebra | pl_PL |
| dc.subject | instrument | pl_PL |
| dc.title | Entropy of Quantum Measurement | pl_PL |
| dc.type | Article | pl_PL |
| dc.page.number | 1181-1196 | pl_PL |
| dc.contributor.authorAffiliation | University of Łódź, Faculty of Mathematics and Computer Sciences | pl_PL |
| dc.references | Von Neumann, J. Mathematische Grundlagen der Quantenmechanik (Mathematical Foundations of Quantum Mechanics); Springer: Berlin, Germany, 1932; Princeton University Press: Princeton, NJ, USA, 1955. | pl_PL |
| dc.references | Bratteli, O.; Robinson, D.W. Operator Algebras and Quantum Statistical Mechanics; Springer: Berllin, Germany and New York, NY, USA, 1979; Volume I. | pl_PL |
| dc.references | Emch, G.G. Algebraic Methods in Statistical Mechanics and Quantum Field Theory; Wiley-Interscience: New York, NY, USA, 1972. | pl_PL |
| dc.references | Haag, R. Local Quantum Physics. Fields, Particles, Algebras; Springer: Berlin, Germany and New York, NY, USA, 1992. | pl_PL |
| dc.references | Haag, R.; Kastler, D. An algebraic approach to quantum field theory. J. Math. Phys. 1964, 5, 848–861. | pl_PL |
| dc.references | Segal, I.E. Postulates for general quantum mechanics. Ann. Math. 1947, 48, 930–948. | pl_PL |
| dc.references | Neshveyev, S.; Størmer, E. Dynamical Entropy in Operator Algebras; Springer: Berlin, Germany and New York, NY, USA, 2006. | pl_PL |
| dc.references | Petz, D.; Ohya, M. Quantum Entropy and Its Use; Springer: Berlin, Germany and New York, NY, USA, 2004. | pl_PL |
| dc.references | Ohya, M.; Watanabe, N. Quantum entropy and its applications to quantum communication and statistical physics. Entropy 2010, 12, 1194–1245. | pl_PL |
| dc.references | Rørdam, M.; Størmer, E. Classification of nuclear C*-Algebras. Entropy in operator algebras. In Encyclopaedia of Mathematical Sciences; Springer: Berlin, Germany and New York, NY, USA, 2002. | pl_PL |
| dc.references | Davies, E.B. Quantum Theory of Open Systems; Academic Press: London, UK and New York, NY, San Francisco, CA, USA, 1976. | pl_PL |
| dc.references | Davies, E.B.; Lewis, J.T. An operational approach to quantum probability. Comm. Math. Phys. 1970, 18, 239–260. | pl_PL |
| dc.references | Segal, I.E. A note on the concept of entropy. J. Math. Mech. 1960, 9, 623–629. | pl_PL |
| dc.references | Umegaki, H. Conditional expectation in an operator algebra, IV (Entropy and information). K¯odai Math. Sem. Rep. 1962, 14, 59–85. | pl_PL |
| dc.references | Busch, P.; Lathi, P.J.; Mittelstaedt, P. The Quantum Theory of Measurement; Lecture Notes in Physics Monographs Volume 2; Springer: Berlin, Germany; New York, NY, USA, 1991. | pl_PL |
| dc.references | Łuczak, A.; Podsędkowska, H. Lüders instruments, generalized Lüders theorem, and some aspects of sufficiency. Int. J. Theor. Phys. 2015, doi:10.1007/s10773-014-2485-y. | pl_PL |
| dc.references | Łuczak, A. Characterization of von Neumann instruments in a theory of quantum measurement. In Proceedings of the 26th Symposium on Mathematical Physics, Toru´n, Poland, 7–10 December 1993; pp. 23–30. | pl_PL |
| dc.references | Lüders, G. Über die Zustandsänderung durch den Messprozess. Ann. Phys. 1951, 8, 322–328. | pl_PL |
| dc.references | Arias, A.; Gheondea, A.; Gudder, S. Fixed points of quantum operations. J. Math. Phys. 2002, 43, 5872–5881. | pl_PL |
| dc.references | Busch, P.; Singh, J. Lüders theorem for unsharp quantum measurements. Phys. Lett. A 1998, 249, 10–12. | pl_PL |
| dc.references | Liu, W.; Wunde, J. Fixed points of commutative Lüders operations. J. Phys. A Math. Theor. 2010, 43, doi:10.1088/1751-8113/43/39/395206. | pl_PL |
| dc.references | Łuczak, A. On ideal measurements and their corresponding instruments on von Neumann algebras. Open Syst. Inf. Dyn. 1999, 6, 325–334. | pl_PL |
| dc.contributor.authorEmail | hpodsedk@math.uni.lodz.pl | pl_PL |
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