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Abstract: In quantum information science, embezzlement refers to the counterintuitive possibility of extracting arbitrary entangled states from a reference state (the "embezzler") via local unitary operations while hardly perturbing the latter. Basic conservation laws imply that an embezzler has infinite entanglement. To study this phenomenon, we consider a pair (M, M’) of a von Neumann algebra and its commutant in standard form as the bipartite system and study how well a given pure state, i.e., a unit vector Ω in the positive cone, performs at the task of embezzling arbitrary entangled states. We find a connection to the flow of weights on M: Ω is good at embezzling if and only if the dual state ω̂ is an approximate fixed point of the flow of weights. In particular, embezzling states correspond to fixed points of the flow of weights, and the type III_1 factor can be uniquely characterized by the property that all states are embezzling. For type III_λ factors, 0<λ<=1, the value of λ can be recovered from the worst-case embezzlement performance of all bipartite pure states. The λ=0 is open. This is joint work with A. Stottmeister, H. Wilming, and R.F. Werner.

Vil du vide, hvad der foregår bag kulisserne hos IMADA? Kom og vær med til 2 x 20 min. inspirerende foredrag, mens du nyder en gratis "afslappet after-work" øl med dine medstuderende, kollega eller lærer. Ved dette IMADA Talks kan du møde lektor Stefan Jänicke og postdoc Konstantin Wernli.

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