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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 38, Fasc. 2,
pages 429 - 440
 

ENTROPIC UPPER BOUND FOR BAYES RISK IN THE QUANTUM CASE

Rafał Wieczorek
Hanna Podsędkowska

Abstract: 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.

2010 AMS Mathematics Subject Classification: Primary: 81P15; Secondary: 81P50.

Keywords and phrases: Bayes risk, probability of detection, quantum measurement, entropy.

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