Entanglement witnesses and geometry of entanglement of two--qutrit states

Abstract

We construct entanglement witnesses with regard to the geometric structure of the Hilbert--Schmidt space and investigate the geometry of entanglement. In particular, for a two--parameter family of two--qutrit states that are part of the magic simplex we calculate the Hilbert--Schmidt measure of entanglement. We present a method to detect bound entanglement which is illustrated for a three--parameter family of states. In this way we discover new regions of bound entangled states. Furthermore we outline how to use our method to distinguish entangled from separable states.

23 pages, 8 figures

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• John Bell and the Nature of the Quantum World
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Bures and Hilbert-Schmidt 2 x 2 Determinantal Moments
• Weyl's Relations, Integrable Matrix Models and Quantum Computation