Abstract
The Weyl operators give a convenient basis of M_n(C) which is also orthonormal with respect to the Hilbert-Schmidt inner product. The properties of such a basis can be generalised to the notion of a nice error basis(NEB), as introduced by E. Knill. We can use an NEB of M_n(C) to construct an NEB for Lin(M_n(C)), the space of linear maps on M_n(C). Any linear map on M_n(C) will then correspond to a n²× n² coefficient matrix in the basis decomposition with respect to such an NEB of Lin(M_n(C)). Positivity, complete (co)positivity or other properties of a linear map can be characterised in terms of such a coefficient matrix.