# Stuttgart 2012 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 67: Quanteneffekte: Verschränkung und Dekohärenz 2

### Q 67.7: Vortrag

### Freitag, 16. März 2012, 15:30–15:45, V7.01

**Arvesons Entanglement Measure in Finite Dimensional Quantum Systems** — •Florian Sokoli and Gernot Alber — Institut für angewandte Physik, Theoretical Quantum Physics Group, Technische Universität Darmstadt

The problem of understanding entanglement is crucial for quantum information theory and applications. However, entanglement is poorly understood at least for multipartite and mixed quantum states. In 2008, the mathematician William Arveson [1] proposed a powerful and elegant way of quantifying entanglement which applies to arbitrary N-partite quantum states and reduces to the so called "projective norm" of density operators in finite dimensional systems. However, in general its computation is difficult. We propose a new technic which can be interpreted as a generalized Schmidt decomposition for multipartite systems. With its help the computation of the projective norm of a large class of quantum states can be reduced to the determination of eigenvalues. These so called gsd-states are characterized by having support on certain subspaces of the underlying Hilbert space. In particular, mixed states are included and this class of states is stable under mixing. We derive a formula for the quantification of the amount of entanglement for multipartite states that arise by tracing out arbitrary subsystems of a special type of gsd-states. [1] William Arveson, arXiv:0804.1140v5