Abstract
Convex polytopes are convex hulls of point sets in the n-dimensional space that generalize two-dimensional convex polygons and three-dimensional convex polyhedra. We concentrate on the class of n-dimensional polytopes in called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness.
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