  The Weyl operators give a convenient basis of $M_n(\mathbb{C})$ 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 $M_n(\mathbb{C})$ to construct an
NEB for $Lin(M_n(\mathbb{C}))$, the space of linear maps on $M_n(\mathbb{C})$.
Any linear map on $M_n(\mathbb{C})$ will then correspond to a $n^2\times n^2$
coefficient matrix in the basis decomposition with respect to such an NEB of
$Lin(M_n(\mathbb{C}))$. Positivity, complete (co)positivity or other properties
of a linear map can be characterised in terms of such a coefficient matrix.
