Lower bounds on the size of quantum automata accepting unary languages

In this paper, we study measure-once 1-way quantum automata accepting unary languages, i.e., of type . We give two lower bounds on the number of states of such automata accepting certain languages. 1. We prove the existence of n-periodic languages requiring states to be recognized. This should be compared with results in the literature stating that every n-periodic language can be recognized with states. 2. We give a lower bound on the number of states of automata accepting the finite language , for a given L. This bound is obtained by using quantum information theory arguments.