Quantum systems with infinitely many degrees of freedom may exhibit an effect known as embezzlement of entanglement, first discovered by van Dam and Hayden in an approximate form.

In the first part of this talk, I will discuss the intimate relation of this effect with the classification of von Neumann algebras, specifically, Connes’ classification of type III factors.

In the second part, I will illustrate that this effect is ubiquitous in quantum many-body systems and quantum field theory.

In particular, the embezzlement of entanglement can be understood as a large-scale effect that only sharply manifests in systems with an unbounded number of

degrees of freedom--comparable to the emergence of sharp macroscopic properties in the thermodynamic limit.

Joint work with Lauritz van Luijk, Reinhard F. Werner, and Henrik Wilming.