On a general concept of sufficiency in von Neumann algebras

• Autorzy: Łuczak A.
• Języki publikacji: EN

Abstrakty

EN

A general question about the sufficiency of a subalgebra of some bigger algebra in the general operator algebra framework, under the assumption that the subalgebra in question is complete with respect to a family of states, is considered. Two particular cases are dealt with: sufficiency for Bayesian discrimination and sufficiency for unbiased estimation with minimal variance. It turns out that in both cases sufficiency is equivalent to the existence of a map from the bigger algebra into the smaller one having some specific properties.

Słowa kluczowe

EN

sufficient subalgebras; normal states; Bayesian discrimination; unbiased estimation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 2
• Strony: 313--324
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Łuczak A.

• Faculty of Mathematics and Computer Science, Łódź University, ul. S. Banacha 22, 90-238 Łódź, Poland

Bibliografia

• [1] S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photon. 1 (2009), pp. 238-278; preprint, arXiv: 0810.1970.
• [2] J. Bergou, U. Herzog, and M. Hillery, Discrimination of quantum states, in: Quantum State Estimation, M. G. A. Paris and J. Řeháček (Eds.), Lecture Notes in Phys., Vol. 649, Springer, Berlin 2004, pp. 417-465.
• [3] F. Buscemi, Comparison of quantum statistical models: equivalent conditions for sufficiency, Comm. Math. Phys. 310 (2012), pp. 625-647.
• [4] A. Chefles, Quantum state discrimination, Contemp. Phys. 41 (2000), pp. 401-430.
• [5] A. Chefles, The quantum Blackwell theorem and minimum error state discrimination, preprint, arXiv: 0907.0866.
• [6] C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, New York-San Francisco-London 1976.
• [7] A. S. Holevo, Statistical decision theory for quantum systems, J. Multivariate Anal. 3 (1973), pp. 337-394.
• [8] A. Jenčová, Quantum hypothesis testing and sufficient subalgebras, Lett. Math. Phys. 93 (2010), pp. 15-27; preprint, arXiv: 0810.4045.
• [9] A. Łuczak, Quantum sufficiency in the operator algebra framework, Internat. J. Theoret. Phys. 53 (2014), pp. 3423-3433.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).