Entropic upper bound for Bayes risk in the quantum case

• Autorzy: Wieczorek R. , Podsędkowska H.

Identyfikatory

DOI

10.19195/0208-4147.38.2.9

• Języki publikacji: EN

Abstrakty

EN

The entropic upper bound for Bayes risk in a general quantum case is presented. We obtained generalization of the entropic Lower bound for probability of detection. Our result indicates upper bound for Bayes risk (in a particular case of loss function – for probability of detection) in a pretty general setting of an arbitrary finite von Neumann algebra. It is also shown under which condition the indicated upper bound is achieved.

Słowa kluczowe

EN

Bayes risk; probability of detection; quantum measurement; entropy

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2018
• Tom: Vol. 38, Fasc. 2
• Strony: 429--440
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Wieczorek R.

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

autor

Podsędkowska H.

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

Bibliografia

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• [6] H. Podsędkowska, Entropy of quantum measurement, Entropy 17 (3) (2015), pp. 1181-1196.
• [7] D. Ruelle, Statistical Mechanics: Rigorous Results, W. A. Benjamin, Inc., New York-Amsterdam 1969.
• [8] M. Tomamichel, R. Colbeck, and R. Renner, A fully quantum asymptotic equipartition property, IEEE Trans. Inform. Theory 55 (12) (2009), pp. 5840-5847.
• [9] H. Umegaki, Conditional expectation in an operator algebra. IV. Entropy and information, Kodai Math. Sem. Rep. 14 (1962), pp. 59-85.
• [10] A. Wehrl, General properties of entropy, Rev. Modern Phys. 50 (2) (1978), pp. 221-260.
• [11] R. Wieczorek, On the form of the optimal measurement for the probability of detection, Internat. J. Theoret. Phys. 54 (12) (2015), pp. 4506-4511.
• [12] S. Yang, J. Lee, and H. Jeong, Entropic lower bound for distinguishability of quantum states, Adv. Math. Phys. (2015), article ID 683658.

Uwagi

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