Abstract
We obtain two new additivity results of quantum channels. The first one is the additivity of the channel R\'enyi information associated with the sandwiched R\'enyi divergence of order α∈[1/2,1). To prove this, we introduce the completely bounded 1→α quasi-norms for completely positive maps, with α∈[1/2,1), and show that it is multiplicative. The additivity/multiplicativity derived here extends and complements the results of Devetak {\it et al} (Commun Math Phys 266:37-63, 2006) and Gupta and Wilde (Commun Math Phys 334:867-887, 2015), which deal with the case α>1. The second one is the additivity of the channel dispersion, which is a quantity related to the second-order behavior of quantum information tasks.