A class of symmetric Bell diagonal entanglement witnesses - a geometric perspective
arXiv:1403.1069 · doi:10.1088/1751-8113/47/42/424033
Abstract
We provide a class of Bell diagonal entanglement witnesses displaying an additional local symmetry -- a maximal commutative subgroup of the unitary group U(n). Remarkably, this class of witnesses is parameterized by a torus being a maximal commutative subgroup of an orthogonal group SO(n-1). It is shown that a generic element from the class defines an indecomposable entanglement witness. The paper provides a geometric perspective for some aspects of the entanglement theory and an interesting interplay between group theory and block-positive operators.
arXiv comment14 pages; Submission to Special Issue of J. Phys. A celebrating 50 years of Bell-nonlocality
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