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.