Operator Algebras and Quantum Information
Description
The past decade has witnessed a burst of interactions between operator algebras and quantum information theory, largely centered around the study of quantum entanglement -- a central notion in quantum information and a key resource in the applications that are driving efforts to develop quantum technologies. While there is a growing depth of understanding of the concept and its many potential uses, the theory and applications of quantum entanglement remains an active, challenging, and fundamental area of investigation in quantum information with relatively little progress having been made in infinite-dimensional and/or operator algebraic quantum systems. Aside from their theoretical importance (general quantum mechanics is rooted in such settings), operator algebras naturally model hybrid classical-quantum systems and numerous modern-day architectures for quantum computing encode quantum information in infinite-dimensional quantum systems. Thus, one can reasonably expect that continued long-term progress in quantum information theory and its connections within quantum physics will depend at least partly on the successful extension of central results in the field to the infinite-dimensional and general operator algebraic settings, with new peculiarities and connections uncovered along the way. This is clearly a desirable goal, and there has been a recent reemergence of activity in this direction, including (hybrid) quantum error correction and privacy, entanglement distillation, entropy theory, non-local games and self-testing, entanglement in quantum field theory, and most notably, connections with, and recent negative solution to, Connes' Embedding Problem -- a major problem in operator algebras dating back to the 1970's. In light of these significant recent advancements and the increasing number of international workshops at the confluence of operator algebras and quantum information, the proposed workshop will be the inaugural meeting of a new annual international conference series entitled ``Operator Algebras and Quantum Information''. (The second meeting will take place at the Mittag-Leffler Institute as part of the Thematic Program on Operator Algebras and Quantum Information (February 4 -- May 22, 2026).) This conference series will create a common international platform to facilitate the exchange of ideas, collaboration, and training of early career researchers. The first meeting will be in honour of Vern Paulsen, on the occasion of his recent retirement. Paulsen made significant contributions to multiple areas of quantum information theory, including entanglement and non-local games and the theory of quantum channels. He also helped train and influence a remarkable number of young researchers in the area. As a result, we aim to bring together operator algebraists and quantum information theorists who are working in the areas of non-local games, infinite-dimensional entanglement, and quantum channels. Participants will be encouraged to discuss recent developments as well as open problems. It will also be an ideal workshop to discuss and set new directions for future studies, and give students and postdocs a unique opportunity to interact with different scientists at the ground level of new potential research directions. Indeed, another focus of this workshop is the training of highly qualified personnel. We also plan to have two invited speakers from the quantum computing industry whose research is connected to the above themes. The exchange of new ideas, fostering of new collaborations and training of young researchers will help to strengthen and expand a diverse research community, and to solidify a common ground for future interactions. We expect the ``Operator Algebras and Quantum Information'' conference series to steadily grow in scope, diversity, and impact. Some recent advancements alluded to above include: - Stabilizer formalism for operator algebra quantum error correction and its applications. - Entanglement cost for infinite-dimensional physical systems. - Local operations, classical communication and state convertibility in von Neumann algebras. - Quantum hypothesis testing in von Neumann algebras. - Approximate quantum channel recovery from approximate relative entropy preservation. - Entanglement measures in algebraic quantum field theory. - Holographic quantum error correction and the anti- de Sitter space/conformal field theory correspondence. - Operator algebraic formulation of self-testing quantum systems. - The resolution in the negative of Connes' Embedding Problem (major open problem in operator algebras for over 40 years). - The resolution in the negative of Tsirelson's problem (major open problem in theoretical physics for over 30 years).