Embezzling entanglement from quantum fields

Embezzlement refers to the counterintuitive possibility of extracting entangled quantum states from a reference state of an auxiliary system (the "embezzler") via local quantum operations while hardly perturbing the latter. We report a deep connection between the mathematical classification of von Neumann algebras and the operational task of embezzling entanglement. This result implies that relativistic quantum fields are universal embezzlers: Any entangled state of any dimension can be embezzled from them with arbitrary precision. This provides an operational characterization of the infinite amount of entanglement present in the vacuum state of relativistic quantum field theories.