Geometry of entanglement witnesses for two qutrits

Details Geometry of entanglement witnesses for two qutrits Geometry of entanglement witnesses for two qutrits

2011-05-24

arxiv.org/abs/1105.4821v1

Open Sys. Information Dyn. 18, 387 (2011)

Physics

Quantum Physics

9 pages

Scientific paper

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 x 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parameterized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement witnesses parameterized by improper rotations from the orthogonal group O(2).

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