Geometry of entanglement witnesses for two qutrits
Quantum Physics
2012-01-31 v1 Mathematical Physics
math.MP
Abstract
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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Cite
@article{arxiv.1105.4821,
title = {Geometry of entanglement witnesses for two qutrits},
author = {Dariusz Chruściński and Filip A. Wudarski},
journal= {arXiv preprint arXiv:1105.4821},
year = {2012}
}
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9 pages