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Explore a comprehensive lecture on quantum protocols, focusing on testing and quantum probabilistically checkable proofs (PCPs). Delve into key concepts such as distance measures, entanglement, compression, and the gap between classical and quantum systems. Learn how these elements come together in the MIP* = RE theorem, which relates to multi-prover interactive proofs with entangled provers. Examine the organization of quantum protocols, compression techniques, and the role of Turing machines in this context. Gain insights from speaker Zhengfeng Ji of the University of Technology Sydney as he presents this complex topic at the Simons Institute.