QLunch: Lauritz van Luijk

Speaker: Lauritz van Luijk from Hannover 

Title: Entanglement, von Neumann algebras and many-body systems

Abstract: I will present recent results on the study of quantum entanglement in systems with infinitely many degrees of freedom, with a focus on many-body systems in the thermodynamic limit. 

Typically quantum systems with infinitely many degrees of freedom do not allow for a description purely in terms of Hilbert spaces. Instead, one describes a system by its observable algebra which, in this talk, we take to be a von Neumann algebra. 

A commuting pair of von Neumann algebras on a joint Hilbert space is regarded as a bipartite system. Every bipartition of a many-body system in the ground state sector (e.g. a 1d spin chain cut into left and right halves) gives rise to such a vN algebraic bipartite system. The algebraic type of the local observable algebras is determined by the large-scale entanglement structure of the ground state. It can be used to detect entanglement properties such as the phenomenon of 'embezzlement of entanglement'. 

I will further discuss the interplay of entanglement properties of bipartite systems and the algebraic type of von Neumann algebras. In particular, I will present a theory of LOCC and a generalization of Nielsen's theorem in the von Neumann algebraic setting and discuss its consequences.

Joint work with Alexander Stottmeister, Reinhard Werner and Henrik Wilming