Thomas Vidick - Connes Embedding Problem, Tsirelson’s Problem, and MIP* = RE

Explore the fascinating world of operator algebras and quantum correlations in this 45-minute lecture by Thomas Vidick for the International Mathematical Union. Delve into the Connes embedding problem and its equivalent reformulations, including Tsirelson's problem. Discover the groundbreaking result MIP^{∗} = RE and its implications for quantum information theory. Learn about the basic approach of separating convex sets and the undecidability of quantum value. Examine key ingredients such as the rigidity of quantum correlations and the role of Probabilistically Checkable Proofs (PCPs) and Multi-prover Interactive Proofs (MIPs) in this negative resolution. Gain insights into the birth of operator algebras and their significance in modern mathematics and theoretical physics.

Intro
The birth of operator algebras
Connes' embedding problem
Equivalent reformulations
Correlations sets
Nonlocal correlations
A negative resolution
The basic approach: separating convex set
Undecidability of the quantum value
Ingredient (1): rigidity of quantum correlations
Ingredient (2): PCPs and MIPS