The Chernoff lower bound for symmetric quantum hypothesis testing
摘要
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.
引用
@article{arxiv.quant-ph/0607216,
title = {The Chernoff lower bound for symmetric quantum hypothesis testing},
author = {Michael Nussbaum and Arleta Szkoła},
journal= {arXiv preprint arXiv:quant-ph/0607216},
year = {2009}
}
备注
Published in at http://dx.doi.org/10.1214/08-AOS593 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)