  We introduce quantum finite state transducers (qfst), and study the class of
relations which they compute. It turns out that they share many features with
probabilistic finite state transducers, especially regarding undecidability of
emptiness (at least for low probability of success). However, like their
`little brothers', the quantum finite automata, the power of qfst is
incomparable to that of their probabilistic counterpart. This we show by
discussing a number of characteristic examples.
