 Applying this definition to the case at hand, i.e.  pairwise to the quantum mechanical distributions \(\mu'(q)\) and \(\mu(q)\) and to \(\nu'(p)\) and \(\nu(p)\) in  (31)  and  (32),  BLW’s final step is to take a supremum over all possible input states \(\ket{\psi}\) to obtain 