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An open question in quantum complexity theory is whether or not the class$\operatorname{MIP}^{co}$, consisting of languages that can be efficientlyverified using interacting provers sharing quantum resources according to thequantum commuting model, coincides with the class $coRE$ of languages withrecursively enumerable complement. We introduce the notion of a qc-modulus,which encodes approximations to quantum commuting correlations, and show thatthe existence of a computable qc-modulus gives a negative answer to a naturalvariant of the aforementioned question.

Approximate traces on groups and the quantum complexity class $\operatorname{MIP}^{co,s}$