Operator Algebras and Quantum Information

The past decade has witnessed a burst of interactions between operator algebras and quantum information theory.  Objects of quantum informational nature, such as channel capacities, quantum game values, perfect strategies, confusability graphs and quantum entropies, were shown to be closely linked to operator spaces, operator systems and C*-algebras, and precise translations between the language of quantum mechanics and that of functional analysis were made, leading to a significant progress in intricate questions from both fields. Arguably the prime examples of such interactions are the equivalence between the Connes Embedding Problem in operator algebra theory and the Tsirelson Problem in theoretical physics. The related Strong Tsirelson Conjecture and a closely related problem on the difference between liminal and finite entanglement was settled using deep pure mathematical techniques.

All of the aforementioned results inscribe in a long historical thread about the behavior of correlations between two non-communicating parties of a quantum experiment, which goes back to the Einstein-Podolsky-Rosen paradox and to its answer given by Bell’s Theorem.

Despite of the dynamics, a number of challenging problems in the area remain open, with many research directions being only at their start. The Program will both investigate specific open questions and explore broader avenues that can lead to qualitative developments, focusing on the following five problem clusters:

• Around Connes Embedding Problem and Tsirelson Problem.
• Operator space techniques in quantum information theory.
• No-signalling correlations and non-local games.
• Quantised discrete structures.
• Challenges in zero-error quantum information.

During the program, there will be  two workshops with thematically focused talks:

March 16-20, 2026: Probabilistic and discrete approaches in Quantum Information Theory

May 18-22, 2026: Operator Algebras and Quantum Information Theory

The multiple recent interactions between Quantum Information Theory and Operator Algebras inspired the start of a new conference series, of which the first meeting is taking place at the University of Waterloo in June 2025. The present conference at the Mittag-Leffler Institute will be the second one in the series. It will highlight new developments in the interface of the two areas, and will comprise a mini-course component directed to early career researchers and PhD students.

During the program, there will be  three mini courses:

February, week 8-9, 2026: The commuting operator model in Quantum Information Theory
by Jason Crann

March, week 10-11, 2026: Non-local games
by Vern Paulsen

March – April, week 13-14, 2026: Limits of discrete structures
by Mahya Ghandehari