Hastings' additivity counterexample via Dvoretzky's theorem

TL;DR

This paper demonstrates that Hastings' counterexample to the additivity conjecture in quantum information theory can be derived using a refined form of Dvoretzky's theorem, linking convex geometry to quantum entropy.

Contribution

It provides a geometric perspective on Hastings' counterexample, connecting convex body sections with quantum entropy additivity issues.

Findings

Hastings' counterexample can be explained via Dvoretzky's theorem.

A sharp version of Dvoretzky's theorem is instrumental in understanding the counterexample.

The approach bridges convex geometry and quantum information theory.

Abstract

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.