Embezzlement of entanglement, quantum fields and the classification of von Neumann algebras

CS/Math Seminar - Lauritz van Luijk, Leibniz Universität Hannover

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 reference. I will explain a deep connection between this operational task and the mathematical classification of von Neumann algebras.

This result implies that relativistic quantum fields are universal embezzlers: Any entangled state of any dimension can be embezzled from them with arbitrary precision. In particular, this provides an operational characterization of the infinite amount of entanglement present in the vacuum state of relativistic quantum field theories and explains the classic result that the vacuum maximally violates Bell's inequalities: Alice and Bob can simply embezzle a maximally entangled qubit pair and perform a Bell measurement.

The talk is based on joined work with A Stottmeister, RF Werner, and H Wilming (see arXiv:2401.07292, arXiv:2401.07299).

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