Quantum Sign Permutation Polytopes

TL;DR

This paper explores the mathematical structure of sign permutation polytopes and their applications in quantum state identification, highlighting their potential for robustness in quantum information processing.

Contribution

It characterizes sign permutation polytopes and links their construction to quantum density matrices, proposing their use in quantum state identification.

Findings

Sign permutation polytopes are characterized mathematically.

Their construction relates to quantum density matrices.

Potential applications in robust quantum state identification.

Abstract

Convex polytopes are convex hulls of point sets in the $n$-dimensional space $\E^n$ that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in $\E^n$ 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.