Small size quantum automata recognizing some regular languages

Given a class {pα|α∈I} of stochastic events induced by M-state 1-way quantum finite automata (1qfa) on alphabet Σ, we investigate the size (number of states) of 1qfa's that δ-approximate a convex linear combination of {pα|α∈I}, and we apply the results to the synthesis of small size 1qfa's. We obtain: