The problem is the norm that you are considering. Taking the largest singular value gives the norm of a matrix acting on the Hilbert space $C^n$, i.e. the norm of the element of the C*-algebra $M_n(C)$. However, what I want to know is the norm of $\Phi$, which is an operator from the C*-algebra to itself. Therefore, the norm should not be given by the singular value decomposition, if I am not mistaken. I would be fine with any way of doing it, and if it is already implemented this would be best. I also do not insist on Mathematica.