The minimum Renyi entropy output of a quantum channel is locally additive

We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter α > 1. While our work extends the results of [11] (in which local additivity was proven for α = 1), it is based on several new techniques that incorporate the multiplicative nature of `p-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Renyi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here can not be extended to Renyi entropies with parameter α < 1.