  Higher dimensional entangled states demonstrate significant advantages in
quantum information processing tasks. Schmidt number is a quantity on the
entanglement dimension of a bipartite state. Here we build families of
k-positive maps from the symmetric information complete positive
operator-valued measurements and mutually unbiased bases, and we also present
the Schmidt number witnesses, correspondingly. At last, based on the witnesses
obtained from mutually unbiased bases, we show the distance between a bipartite
state and the set of states with Schmidt number less than k.
