Düsseldorf 2007 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 18: Quanteninformation (Verschränkung und Dekohärenz I)

Q 18.4: Vortrag

Dienstag, 20. März 2007, 11:30–11:45, 5L

Covariance matrices and the separability problem — Otfried Gühne¹, Philipp Hyllus^2,3, •Oleg Gittsovich^4,1, and Jens Eisert³ — ¹Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Österreich — ²Institut für Theoretische Physik, Universität Hannover, Appelstrasse 2, 30167 Hannover, Deutschland — ³QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, UK and Institute for Mathematical Sciences, Imperial College London, Prince's Gate, London SW7 2PE, UK — ⁴Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Österreich

The separability problem deals with a question to decide whether a given state is entangled or separable, which is very important from the point of view of applicability of the quantum information theory. This task belongs to the one of the still unsolved theoretical problems, which has received a significant amount of attention in recent years. In this talk I will present a new unifying approach to the separability problem for finite dimensional systems. Our method uses a representation of a quantum state by a covariance matrix of suitable observables. On the one hand, our approach leads to entanglement criteria that detect all entangled states of two qubits, as well as indeed many bound entangled states and, on the other hand, provides a framework to link and understand several existing criteria like cross-norm (or realignment) criterion, a recent criterion using Bloch representation or the local uncertainty relations.