A quantum complexity approach to the Kirchberg Embedding Problem

TL;DR

This paper explores the implications of a positive solution to the Kirchberg Embedding Problem (KEP) on quantum complexity, linking it to nonlocal games and almost-commuting strategies.

Contribution

It establishes two quantum complexity consequences of KEP, connecting operator algebra embedding problems with quantum nonlocal game strategies.

Findings

Two quantum complexity consequences of KEP are derived.

Connections between KEP and nonlocal game strategies are demonstrated.

Implications for quantum complexity theory are discussed.

Abstract

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\cal O_2$. 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.