Berlin 2005 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantum Information Theory

MP 9.2: Fachvortrag

Mittwoch, 9. März 2005, 14:20–14:40, TU MA141

Entanglement in fermionic systems and its application to spin chain models — •Dirk Schlingemann — Institute for Mathematical Physics, Technical University of Braunschweig

The concept of entanglement in fermionic systems is investigated. We consider a bipartite fermionic system, that is, the fermion fields of Alice’s system anti-commute with the fermion fields of Bob’s. Thus Alice’s observables, which are generated by even products of fermion fields, commute with the observables of Bob. Restricting to observables, we are faced with a bipartite system in the usual sense.

The entanglement of a bipartite fermion state is given by the entanglement of its restriction to the corresponding observable algebras. The main problem is now to compute explicitly the standard entanglement measures, like entanglement of formation, for the restricted state. Note that the restricted state is not pure in general although it may be pure on the fermion algebra. Even if the given state is quasi-free (determined by the correlation function of two fermi field operators), we need to find optimal convex decompositions into pure states which need not to be quasi-free.

To overcome this difficulty we show, by using the concept of “twisted EPR doubles", that there is a quasi-free state for which the restriction to the observable part is indeed maximally entangled. Then we introduce an appropriate fidelity which measures how much a given pure state (pure on the fermion algebra) deviates from the maximally entangled one.

The results are applied to ground states of spin chain models which are related to quasi-free states via the Jordan-Wigner transformation.