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Entropic upper bound for Bayes risk in the quantum case

Wieczorek R., Podsędkowska H.

Probability and Mathematical Statistics

2018

Vol. 38, Fasc. 2

429--440

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.