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.
翻译:Kirchberg 嵌入问题( KEP) 询问每个 C* 代数是否都嵌入了Cuntz代数的超能力 $\ cal O_2$。 受最近利用量子复杂性结果MIP<unk> RE反驳 Connes 嵌入问题的影响,我们确定了对 KEP 的积极解决方案的两种量子复杂性后果。 这两个结果都涉及到几乎与非本地游戏的组合策略。</s>