An open question in quantum complexity theory is whether or not the class $\operatorname{MIP}^{co}$, consisting of languages that can be efficiently verified using interacting provers sharing quantum resources according to the quantum commuting model, coincides with the class $coRE$ of languages with recursively enumerable complement. We introduce the notion of a qc-modulus, which encodes approximations to quantum commuting correlations, and show that the existence of a computable qc-modulus gives a negative answer to a natural variant of the aforementioned question.
翻译:量子复杂度理论的一个未决问题是,由能根据量子通量模型共享量子资源的互动证明人所能有效核实的语言构成的等级 $\ operatorname{MIP ⁇ ç ⁇ co}$ 是否与具有递归性可量化补充语言的等级 $coRE$相吻合。 我们引入了qc-moluls的概念,该概念将近似值编码为量子通量相关关系,并表明可计算qc-moluls的存在给上述问题的自然变体提供了否定的答案。