From Quantum Query Complexity to State Complexity
  State complexity of quantum finite automata is one of the interesting topics in studying the power of quantum finite automata. It is therefore of importance to develop general methods how to show state succinctness results for quantum finite automata. One such method is presented and demonstrated in this paper. In particular, we show that state succinctness results can be derived out of query complexity results. 
Shenggen Zheng, Daowen Qiu
cs.CC quant-ph