Embezzlement of entanglement and the classification of von Neumann algebras

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• Alexander Stottmeister (Leibniz Universität Hannover)
• Monday 02 December 2024, 14:50-15:30
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

I will discuss the embezzlement of entanglement in the setting of von Neumann algebras and how it relates to the classification of the latter. Embezzlement (of entanglement), following van Dam and Hayden, is the task of producing any entangled state to arbitrary precision from a shared entangled resource state, the embezzling state, using local operations without communication while perturbing the resource arbitrarily little.  It can be shown that Connes’ classification of type III factors can be given a quantitative operational interpretation in terms of embezzlement. This quantification implies that: 1) semifinite factors (type I or II) cannot host embezzling states, 2) all type III factors, apart from some type III _0 factors, host embezzling states, 3) type III _1 factors are characterized as ‘universal embezzlers’, meaning that every normal state is embezzling. These results follow from a one-to-one correspondence between embezzling states and invariant states on the flow of weights. It can be demonstrated that universal embezzlement occurs in various relevant physical models, such as critical spin chains and quantum field theories. The latter observation provides a simple explanation for why relativistic quantum field theories maximally violate Bell inequalities. If time permits, I will also discuss the relationship between embezzling states and embezzling families (originally discovered by van Dam and Hayden), as well as some recent findings in the multipartite setting. This is joint work with Lauritz van Luijk, Reinhard F. Werner, and Henrik Wilming.

This talk is part of the Isaac Newton Institute Seminar Series series.

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