This page contains my handwritten lecture notes for 6.S979, taught in the fall of 2020. For MIT students, the official course website is on Canvas.
A list of suggested readings for the final project is available here.
Lecture 1: Intro and quantum basics
Lecture 2: The CHSH game
Lecture 3: Three proofs of Tsirelson's bound
Lecture 4: CHSH as a self-test
Lecture 5: Applications of self-testing
Lecture 6: Contextuality and the magic square
Lecture 7: The Wigner function and the failure of magic square for qudits
Lecture 8: Classical and quantum correlations, and Tsirelson's SDP for XOR correlations
Lecture 9: More on Tsirelson's SDP for XOR correlations
Lecture 10: The NPA hierarchy
Lecture 11: Separating finite and infinite dimensional correlations
Lecture 12: Guest lecture by Adam Bene Watts on multiplayer XOR games
Lecture 13: Intro to interactive proofs, and the MIP perspective on correlations
Lecture 14: More on computability and correlations, and the connection between MIP and CSPs
Lecture 15: An MIP based on the Hadamard code
Lecture 16: The BLR test
Lecture 17: Quantum BLR and MIP*
Lecture 18: More on quantum BLR, and connections to self-testing
Lecture 19: The Pauli Brading Test
Lecture 20: Delegating BQP computations in the MIP* model
Lecture 21: Introspection and compression of MIP* protocols
Lecture 22: More on compression
Lecture 23: Showing MIP* = RE, and an aside on on non-signaling MIP
Lecture 24: Cryptographic tests of quantum ness and the Mahadev verification protocol
Lecture 25: The Mahadev protocol continued
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