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Lecture 1: Entanglement in quantum interactive proofs (tutorial)

Presented by: 
T Vidick Massachusetts Institute of Technology
Monday 2nd September 2013 - 10:00 to 11:00
INI Seminar Room 1
In 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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons