Now suppose the provers have entangled quantum bits. This question has a long history that culminates in the MIP* = RE paper earlier this year by Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, Henry Yuen showing that every proof of any length can be proven in this model. Incredible!
But wait, why is there a new version 2 dated last week? Turns out the MIP* = RE paper relied on a 2016 paper by Vidick which was later discovered to have a bug. No worries, as the authors of the MIP* = RE paper got around this issue by a quantum analysis of a low-degree test from that old Babai-Fortnow-Lund paper.