Correlation Chains and Quantum Hierarchies (23rit012)


Jason Crann (Carleton University)


The Banff International Research Station will host the "Correlation Chains and Quantum Hierarchies" workshop in Banff from September 24 to October 1, 2023.

The question about the genuine distinction between classical and quantum mechanics, notably raised by Einstein in the 1930's, was definitively settled in the 1960's through the celebrated Bell Theorem. Since then, other models of quantum physics, utilising seemingly larger resource classes, have appeared, with the prime example the commuting operator model. Its genuinely greater power, when compared to the more conventional tensor product model, has been formally proved only recently, simultaneously settling an over 40 year old open problem in pure mathematics, known as the Connes Embedding Problem.

In the current project, we aim to use techniques from operator theory to enrich the toolkit available to distinguish between these different quantum mechanical models. As a primary instrument, we will use non-local games, which have in the past couple of decades become prominent in quantum information theory. As a result of our research, we expect to strengthen the existing links between operator algebra theory and quantum computing, leading to new pure mathematical directions, and developing more mathematical tools for use in theoretical physics.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), and Alberta's Advanced Education and Technology.