The Chernoff lower bound for symmetric quantum hypothesis testing
Michael Nussbaum and Arleta Szkola
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Submission date: 02. Aug. 2006 (revised version: August 2007)
published in: The annals of statistics, 37 (2009) 2, p. 1040-1057
DOI number (of the published article): 10.1214/08-AOS593
Keywords and phrases: quantum hypothesis testing, quantum Chernoff bound, Bayesian error probability
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We consider symmetric hypothesis testing, where the hypotheses are allowed to be arbitrary density operators in a finite dimensional unital -algebra capturing the classical and quantum scenarios simultaneously. We prove a Chernoff type lower bound for the asymptotically achievable error exponents. In the case of commuting density operators it coincides with the classical Chernoff bound. Moreover, the bound turns out to be tight in some non-commutative special cases, too. The general attainability of the bound is still an open problem.