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={Igor Devetak and Marius Junge and Christopher King and Mary Beth Ruskai},
  journal={Communications in Mathematical Physics},
  year={2006},
  volume={266},
  pages={37-63}
}
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
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