Quantum correlations, complexity theory, and the Connes embedding problem
Nonlocal correlations were introduced by John Bell in 1964 as a way to operationally distinguish quantum mechanics from classical models of the world. Since then, they have become an important tool in probing the structure of quantum mechanics. An open problem in this area, arising from the work of Boris Tsirelson, was to determine whether the set of correlations arising from the so-called "commuting operator" model of quantum nonlocality is strictly larger than the set arising from the "tensor product" model. This question, in addition to its intrinsic interest, is also surprisingly connected to the Connes embedding problem, an open problem in operator algebras: a positive answer to the Connes problem implies that the two correlation sets in Tsirelson's problem are equal. In this talk I will present recent work resolving these problems using computational complexity theory.
Based on joint work with Zhengfeng Ji, Thomas Vidick, John Wright, and Henry Yuen (https://arxiv.org/abs/2001.04383)