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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 8: Quantum Field Theory II

MP 8.1: Invited Talk

Wednesday, March 20, 2024, 09:30–10:00, HL 001

Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras — •Alexander Stottmeister — Leibniz University 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 latter. We report a deep connection between the mathematical classification of von Neumann algebras and the operational task of embezzling entanglement: The performance of a general state at the task of embezzling is measured by the flow of weights. In particular, embezzling states, having the best performance, are fixed points of the flow of weights. For a type III factor, its subtype is precisely recovered by the worst possible performance. Our result implies, under typical assumptions, that relativistic quantum fields are universal embezzlers, thereby providing an operational characterization of the infinite amount of entanglement present in the vacuum state: Any entangled state of any dimension can be embezzled from them with arbitrary precision.

This is joint work with L. van Luijk, H. Wilming, and R.F. Werner.

Keywords: Entanglement; Embezzlement; Quantum Field Theory; Von Neumann algebras; Modular Theory