Résume | MIP* and RE are complexity classes, similar but larger to the more well-known P, NP, etc. The equality in the title implies that a natural optimization problem that originates in the study of nonlocality in quantum mechanics is undecidable. Due to prior work by many others this undecidability implies a negative answer to multiple conjectures in quantum information (Tsirelson's problem) and operator algebras (Connes' Embedding Problem (CEP), Kirchberg's QWEP).
In the talk I will explain the characterization MIP* = RE and its connection to the study of nonlocality, Tsirelson's problem, and operator algebras. I will give an overview of the proof of MIP* = RE, which involves reducing the Halting Problem to the problem of approximating the supremum of a linear function on certain quantum correlation sets.
Based on joint work with Ji, Natarajan, Wright and Yuen available as arXiv:2001.04383. |