Abstract: 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 a key role. Moreover, evidence of superadditivity can be found even if the additivity violation itself is too small to be seen numerically.
A program to to test 3-state qubit channels for superadditivity of the Holevo capacity will be described. In addition the proof of local additivity will be sketched with several significant simplifications.