A new kind of mixed character sums and their applications

In this paper, as a generalization the famous Gaussian sums, we introduce a new kind of mixed character sums and their applications in the constructions of Mutually unbiased bases (MUBs) and signal sets. It is well-known that MUBs have significant applications in quantum information processing and other fields. However, only a few constructions of MUBs are known in the literature. In this note, we provide a recursive constructions of approximately mutually unbiased bases. Meanwhile, we present some constructions of asymptotically optimal signal sets by using the mixed character sums.