Geometrical aspects of entanglement

Abstract

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.

31 pages, 6 figures

References in corpus (2)

• Constructing N-qubit entanglement monotones from anti-linear operators
• Towards efficient algorithm deciding separability of distributed quantum states

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