A relation between completely bounded norms and conjugate channels

Abstract

We show a relation between a quantum channel $\Phi$ and its conjugate ${\Phi }^C$, which implies that the $p\to p$ Schatten norm of the channel is the same as the $1\to p$ completely bounded norm of the conjugate. This relation is used to give an alternative proof of the multiplicativity of both norms.

5 pages, we make a connection between quant-ph/0506196 and the papers quant-ph/0509101 and quant-ph/0509126

References in corpus (4)

• Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps
• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity
• On complementary channels and the additivity problem
• A Note on the p->q norms of Completely Positive Maps

Cited by in corpus (2)

• Multiplicativity of completely bounded $p$-norms implies a strong converse for entanglement-assisted capacity
• Computing Stabilized Norms for Quantum Operations via the Theory of Completely Bounded Maps