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April 2009 The Chernoff lower bound for symmetric quantum hypothesis testing
Michael Nussbaum, Arleta Szkoła
Ann. Statist. 37(2): 1040-1057 (April 2009). DOI: 10.1214/08-AOS593


We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the asymptotic rate exponents of Bayesian error probabilities. The bound represents a quantum extension of the Chernoff bound, which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set. In our framework, the classical result is reproduced if the two hypothetic density operators commute.

Recently, it has been shown elsewhere [Phys. Rev. Lett. 98 (2007) 160504] that the lower bound is achievable also in the generic quantum (noncommutative) case. This implies that our result is one part of the definitive quantum Chernoff bound.


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Michael Nussbaum. Arleta Szkoła. "The Chernoff lower bound for symmetric quantum hypothesis testing." Ann. Statist. 37 (2) 1040 - 1057, April 2009.


Published: April 2009
First available in Project Euclid: 10 March 2009

zbMATH: 1162.62100
MathSciNet: MR2502660
Digital Object Identifier: 10.1214/08-AOS593

Primary: 62G10, 62P35

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.37 • No. 2 • April 2009
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