The maximum output p-norm of quantum channels is not multiplicative for any p>2

TL;DR

This paper demonstrates that for any p>2, the maximum output p-norm of quantum channels does not follow a multiplicative property, using counterexamples derived from approximately randomising maps.

Contribution

It provides the first proof that the maximum output p-norm is not multiplicative for all p>2, challenging previous conjectures in quantum information theory.

Findings

Counterexamples from approximately randomising maps

Non-multiplicativity for p>2

Implications for quantum channel capacity

Abstract

We prove the claim made in the title by showing that approximately randomising maps of large dimension are counterexamples to the multiplicativity conjecture.