CB-norm estimates for maps between noncommutative $L_p$-spaces and quantum channel theory

TL;DR

This paper develops sharp embedding techniques for noncommutative $L_p$-spaces using quantum information theory and applies them to determine capacities of quantum channels, revealing nonmultiplicative behaviors.

Contribution

It introduces novel CB-norm estimates for maps between noncommutative $L_p$-spaces and applies these to analyze quantum channel capacities.

Findings

Exact capacity of the quantum erasure channel computed

Nonmultiplicative capacity results shown for the depolarizing channel

Sharp embeddings between noncommutative $L_p$-spaces established

Abstract

In the first part of this work we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative $L_p$-spaces. Then, we use these estimates to study the classical capacity with restricted assisted entanglement of the quantum erasure channel and the quantum depolarizing channel. In particular, we exactly compute the capacity of the first one and we show that certain nonmultiplicative results hold for the second one.