Maximally nonlocal subspaces

Abstract

A nonlocal subspace is a subspace within the Hilbert space of a multi-particle system such that every state violates a given Bell inequality . Subspace is maximally nonlocal if each such state violates to its algebraic maximum. We propose ways by which states with a stabilizer structure of graph states can be used to construct maximally nonlocal subspaces, essentially as a degenerate eigenspace of Bell operators derived from the stabilizer generators. Two cryptographic applications—to quantum information splitting and quantum subspace certification—are discussed.