MIP* = RE Part 2: PCPs and Introspection

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Claim: MIP contains nondeterministic doubly-exponential time (AnyExp) and the techniques extend to the full compression that yields MIP = RE. Key tools are quantum low-degree test and introspection together with PCP composition. The protocol forces provers to share exponentially many entangled bits (modeled as EPR boxes), use total X/Z measurements to introspectively sample exponentially long questions while the verifier sees only polynomial-size queries, then uses PCP-based answer reduction. The compression theorem preserves completeness, soundness gaps and entanglement lower bounds.

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" chapters (17)

1. 0:00Introduction
2. 0:35MIP
3. 3:14The 163 coloring problem
4. 5:47MIP Star
5. 10:58QA
6. 14:13Encoding
7. 20:12Line vs Point Low Degree
8. 26:17PCP Outline
9. 27:20Question Reduction
10. 29:30Shared Randomness
11. 32:28entangled quantum states
12. 34:03quantum low degree test
13. 36:14EPR toy model
14. 43:36Summary
15. 50:13Answer Reduction
16. 52:54Compression
17. 55:46Compression Theorem