Completely positive linear maps on complex matrices

A linear map Φ from $\text{M}$_n to $\text{M}$_m is completely positive iff it admits an expression $\text{Φ(A)=Σ}{}_{\mathrm{i}}\text{V}{}^1{}_{\mathrm{i}}\text{AV}{}_{\mathrm{i}}$ where V_i are n×m matrices.