Title: The MIPco=coRE conjecture and Tracially embedded strategies.
Abstract: Quantum non-local games have been used to model quantum entanglement. Famously, Ji et al. have shown that MIP*=RE, or approximating the optimal success rate of a non-local game under finite-dimensional, tensor product strategies, is uncomputable, and this gives a negative answer to the Connes embedding problem in von Neumann algebra. Thus, a natural follow-up question is whether approximating the optimal success rate of a non-local game under the infinite-dimensional commuting operator setting is also uncomputable. In this talk, I will introduce the MIPco=coRE conjecture, and I will also introduce a subclass of commuting operator strategies known as the Tracially embedded strategies. Tracially embedded strategies are a subset of the commuting operator strategies that, in a quantum information sense, have many similarities to a finite-dimensional tensor product strategy. Using this new characterization, I will discuss how some of the ingredients from proving the MIP*=RE theorem can be generalized to the commuting operator mode and how this can be used to tackle the MIPco=coRE conjecture. This talk is based on the paper arXiv:2304.01940.