Quantum information and computing is an interdisciplinary research area which seeks to leverage quantum mechanical phenomena for information processing purposes, surpassing the capabilities of conventional technologies. One of the key sources of quantum advantages and speed-ups is the phenomenon of quantum entanglement which allows distant parties to correlate their behaviors beyond conventionally reachable limits. It turns out, however, that entanglement-assisted strategies are hard to understand and their analysis gives rise to complex mathematical problems. As a result, we are yet to understand the full potential that entanglement can bring in the context of information processing.
Nonlocal games provide a rigorous general framework for studying the power and limitations of quantum entanglement in a setting with distributed agents. Similar games are well-established tools within the disciplines of theoretical computer science, cryptography, and foundations of physics. During the past decade we have seen that mathematical structures arising from entanglement-assisted strategies for nonlocal games can be naturally interpreted and studied using tools from other areas of mathematics like operator algebras and quantum groups. Most notably, one of the central problems in operator algebras, the 50-year-old Connes' Embedding Problem, was recently resolved using complexity theoretic analysis of nonlocal games.
Nonlocal games is a relatively new topic with no existing text book and key results and techniques being scattered across different research papers. Additionally, due to rich connections to computer science and physics, the range of techniques used in this context is unusually broad. With this Mastercass our goal is to gather a team of world-leading experts with different expertise who will introduce the topic of nonlocal games along with the known beautiful connections to different areas of study.
The primary audience is Master and PhD students.