# Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

@article{Devetak2006MultiplicativityOC,
title={Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result},
author={I. Devetak and M. Junge and C. King and M. Ruskai},
journal={Communications in Mathematical Physics},
year={2006},
volume={266},
pages={37-63}
}
• I. Devetak, +1 author M. Ruskai
• Published 2006
• Mathematics, Physics
• Communications in Mathematical Physics
AbstractWe prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12) − S(γ1) is restricted to states of the form $$(\mathcal{I} \otimes \Phi)\left( | \psi \rangle \langle \psi | \right)$$. We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatten p-norm on matrices, and give… Expand