A quantum complexity approach to the Kirchberg Embedding Problem

Abstract

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra ${\mathcal{O}}_2$. Motivated by the recent refutation of the Connes Embedding Problem using the quantum complexity result MIP*=RE, we establish two quantum complexity consequences of a positive solution to KEP. Both results involve almost-commuting strategies to nonlocal games.

A referee pointed out that the first theorem can be obtained using elementary means in a manner not connected to the KEP. The second result will be incorporated into a new paper that will appear on the arxiv shortly