Succinct Perfect Zero-knowledge for MIP*

In the recent breakthrough result of Slofstra and Mastel (STOC'24), they show that there is a two-player one-round perfect zero-knowledge MIP* protocol for RE. We build on their result to show that there exists a succinct two-player one-round perfect zero-knowledge MIP* protocol for RE with polylog question size and O(1) answer size, or with O(1) question size and polylog answer size. To prove our result, we analyze the four central compression techniques underlying the MIP*= RE proof (Ji et al. '20) -- question reduction, oracularization, answer reduction, and parallel repetition -- and show that they all preserve the perfect (as well as statistical and computational) zero-knowledge properties of the original protocol. Furthermore, we complete the study of the conversion between constraint-constraint and constraint-variable binary constraint system (BCS) nonlocal games, which provide a quantum information characterization of MIP* protocols. While Paddock (QIP'23) established that any near-perfect strategy for a constraint-variable game can be mapped to a constraint-constraint version, we prove the converse, fully establishing their equivalence.