Maximally nonlocal subspaces

Abstract

A nonlocal subspace ${\mathcal{H}}_{NS}$ is a subspace within the Hilbert space ${\mathcal{H}}_n$ of a multi-particle system such that every state $\psi \in {\mathcal{H}}_{NS}$ violates a given Bell inequality $\mathcal{B}$. Subspace ${\mathcal{H}}_{NS}$ is maximally nonlocal if each such state $\psi$ violates $\mathcal{B}$ 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.

Accepted for publication in J. Phys. A; 8 pages, 1 figure

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