MIP* = RE Part 1: The Quantum Low-Degree Test

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" summary

Shows a concrete protocol that self-tests for 2^n EPR pairs by certifying Pauli relations on many qubits. It combines the magic‑square subtest to force anti‑commutation, a linearity/low‑degree subtest to certify multiplicative relations, and consistency checks, so the provers’ observables form an approximate representation of the n‑qubit Pauli group. Approximate relations are then rounded to an exact representation (Gowers–Hatami / Fourier‑style arguments), yielding an isometry that maps the state to many EPR pairs; the quantum low‑degree test makes this communication efficient.

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" chapters (10)

1. 0:00Intro
2. 1:32Nonlocal games and MIP
3. 5:01MIP*: the complexity landscape
4. 6:27Upper-bounding MIP*: challenges
5. 15:24Outline
6. 23:58Magic Square: the Quantum Strategy
7. 31:11Self-testing through representation theory
8. 33:49Magic square as a self-test: the analysis
9. 47:19Testing the relations: anticommutation
10. 54:39Testing consistency