The local additivity of minimal output entropy can be extended to local additivity of maximal relative entropy with respect to a fixed reference state. This can be exploited to test channels for superadditivity of Holevo capacity with numerical effort comparable to searching for the minimal output entropy. Local maxima which do not arise from product inputs play an important role.

This talk will be divided into two parts. First we sketch the Gour-Friedland proof of local additivity with several significant simplifications.

Second, we describe a program to test 3-state qubity channels for superadditivity of the Holevo capacity.