Geometrical aspects of entanglement

Details Geometrical aspects of entanglement Geometrical aspects of entanglement

2006-05-08

arxiv.org/abs/quant-ph/0605079v1

Physics

Quantum Physics

31 pages, 6 figures

Scientific paper

We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and non-unitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability, and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.

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