A class of symmetric Bell diagonal entanglement witnesses—a geometric perspective
Dariusz Chruściński · Journal of Physics A Mathematical and Theoretical · 2014
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 . 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 in . This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.