  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.
