Quantum entanglement and nonlocal games

Nonlocal games provide a rigorous general framework for studying the power and limitations of quantum entanglement in settings involving distributed agents. Such games are well-established tools in theoretical computer science, cryptography, and the foundations of physics. Over the past decade, it has become clear that mathematical structures arising from entanglement-assisted strategies for nonlocal games can be naturally interpreted and studied using tools from other areas of mathematics, such as operator algebras and quantum groups. Most notably, the 50-year-old Connes Embedding Problem — a central problem in functional analysis, and more specifically in operator algebras — was recently resolved using a complexity-theoretic analysis of nonlocal games.

Nonlocal games are a relatively new topic, with no existing textbook, and key results and techniques are scattered across many research papers. Additionally, because of their rich connections to computer science and physics, the range of techniques used in this context is unusually broad. The goal of this lecture is to introduce the topic of nonlocal games, together with its beautiful known connections to different areas of study.

This is a new course that will start in the summer term of 2026/2027.