  In this note, we generalize the results of arXiv:0901.2703v1 We show that all
one-way quantum finite automaton (QFA) models that are at least as general as
Kondacs-Watrous QFA's are equivalent in power to classical probabilistic finite
automata in this setting. Unlike their probabilistic counterparts, allowing the
tape head to stay put for some steps during its traversal of the input does
enlarge the class of languages recognized by such QFA's with unbounded error.
(Note that, the proof of Theorem 1 in the abstract was presented in the
previous version (arXiv:0901.2703v1).)
