Lecture 1: Entanglement in quantum interactive proofs (tutorial)
Seminar Room 1, Newton Institute
AbstractIn the first lecture I will present the reasonably well-understood topic of entanglement in XOR games. We will review results by Tsirelson and Slofstra which provide lower and upper bounds on the dimension of entanglement required to play (near-)optimally. These results are obtained through connections with semidefinite programming and the theory of C*-algebras.
In the second lecture I will move to more general classes of games. I will introduce an interesting "universal" class of entangled states, embezzlement states, and discuss some of their properties. I will present some lower bounds on entanglement dimension, leaving the proof of upper bounds as an exercise to the audience. Time permitting I will connect these results to the complexity theory of multi-prover interactive proofs.
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