The minimum Renyi entropy output of a quantum channel is locally additive (1601.00982v2)

Abstract: We show that the minimum Renyi entropy output of a quantum channel is locally additive for Renyi parameter alpha>1. While our work extends the results of 10, 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 global effects of quantum channels. Interestingly, the approach presented here can not be extended to Renyi entropies with parameter alpha<1.