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

TL;DR

This paper proves that the minimal Renyi entropy of order 2 is additive for PPT-inducing channels, extending the understanding of entropy properties in quantum information theory.

Contribution

It establishes additivity of the minimal RE2 output for PPT-inducing channels and demonstrates the applicability of techniques to other channels.

Findings

Additivity of minimal RE2 output for PPT-inducing channels.

Techniques applicable to depolarizing and transpose depolarizing channels.

Explicit calculations for Werner-Holevo 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.