von Neumann algebraic quantum information theory and entanglement in infinite quantum systems

In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems. But are there different forms of infinite entanglement?

In the first part of my talk, I will present a von Neumann algebraic framework for studying information-theoretic properties of infinite systems. Using this framework, we find operational tasks that distinguish different forms of infinite entanglement, and, by analysing these tasks, we show that the type classification of von Neumann algebras (types I, II, III, and their respective subtypes) is in 1-to-1 correspondence with operational entanglement properties. Our findings promote the type classification from mere algebraic bookkeeping to a classification of infinite quantum systems based on their operational entanglement properties.

In the second part, I will discuss what is known about the type classification of the von Neumann algebras arising in quantum many-body systems. Together with our results, this identifies new operational properties, e.g., embezzlement of entanglement, of well-known physical models, e.g., the critical transverse-field Ising chain or suitable Levin-Wen models.

Joint work with: Alexander Stottmeister, Reinhard F. Werner, and Henrik Wilming