Convex Trace Functions on Quantum Channels and the Additivity Conjecture

TL;DR

This paper investigates the structure of convex trace functions on quantum channels, extending the additivity problem in quantum information theory, and proves that all operator convex functions are additive for a specific quantum channel in 3x3 dimensions.

Contribution

It generalizes the additivity problem to convex trace functions and establishes that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions.

Findings

Operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions.

The set of convex functions attaining maxima on unentangled inputs is characterized.

The results include known additivity results as special cases.

Abstract

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are "additive" in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.