Approximate traces on groups and the quantum complexity class MIPco,s

An open question in quantum complexity theory is whether or not the class 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.