MIP* = RE

Note from the Research Highlights Co-Chairs: A paper appearing in Communications is usually peer-reviewed prior to publication. The following unusual that it still under review. However, result has generated enormous excitement research community, and came strongly nominated by SIGACT, a nomination seconded external reviewers. complexity class NP characterizes collection of computational problems have efficiently verifiable solutions. With goal classifying seem lie beyond NP, starting 1980s theorists considered extensions notion efficient verification allow for use randomness (the MA), interaction IP), possibility interact with multiple proofs, or provers MIP). study these led celebrated PCP theorem its applications hardness approximation design cryptographic protocols. In this work, we fourth modification originates quantum entanglement. We prove surprising every problem recursively enumerable, including Halting problem, can be verified classical probabilistic polynomial-time verifier interacting two all-powerful but noncommunicating sharing resolves long-standing open foundations mechanics (Tsirelson's problem) operator algebras (Connes' embedding problem).