Additivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels

Abstract

We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose (PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.