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The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into anultrapower of the Cuntz algebra $\cal O_2$. Motivated by the recent refutationof the Connes Embedding Problem using the quantum complexity result MIP*=RE, weestablish two quantum complexity consequences of a positive solution to KEP.Both results involve almost-commuting strategies to nonlocal games.

A quantum complexity approach to the Kirchberg Embedding Problem