Maximally nonlocal subspaces

TL;DR

This paper introduces the concept of maximally nonlocal subspaces within multi-particle quantum systems, constructed using stabilizer states, with applications in quantum cryptography such as information splitting and subspace certification.

Contribution

It proposes methods to construct maximally nonlocal subspaces using stabilizer structures of graph states, extending the understanding of nonlocality in quantum subspaces.

Findings

Construction of maximally nonlocal subspaces using stabilizer states

Identification of these subspaces as eigenspaces of Bell operators

Application to quantum cryptography protocols

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.