  One of the properties of Kondacs-Watrous model of quantum finite automata
(QFA) is that the probability of the correct answer for a QFA cannot be
amplified arbitrarily. In this paper, we determine the maximum probabilities
achieved by QFAs for several languages. In particular, we show that any
language that is not recognized by an RFA (reversible finite automaton) can be
recognized by a QFA with probability at most 0.7726...
