  We apply the generalised concept of witness operators to arbitrary convex
sets, and review the criteria for the optimisation of these general witnesses.
We then define an embedding of state vectors and operators into a
higher-dimensional Hilbert space. This embedding leads to a connection between
any Schmidt number witness in the original Hilbert space and a witness for
Schmidt number two (i.e. the most general entanglement witness) in the
appropriate enlarged Hilbert space. Using this relation we arrive at a
conceptually simple method for the construction of Schmidt number witnesses in
bipartite systems.
