Recently, Ji et al. gave a negative answer to the Connes embedding problems by showing that MIP*=RE where the complexity class MIP* corresponds to an interactive proof system where the provers are given access to the tensor product model of entanglement. A natural follow-up question is whether the same uncomputability results also hold for the complexity class MIPco, a variant of MIP* where the provers are given access to the commuting operator model of entanglement instead. We show that this conjecture is true, and the complexity class MIPco is equal to coRE, the complexity class which is complete with respect to the non-halting problem. In this talk, I will sketch the proof for MIPco=coRE and describe some of the operator algebraic tools used to show this conjecture.

This work is supported by ERC STG grant 101040624-ASC-Q.