Deterministic all-versus-nothing proofs of Bell nonlocality based on non-stabilizer states

Abstract

The all-versus-nothing proof of Bell nonlocality is a kind of mainstream demonstration of Bell's theorem without inequalities. Two kinds of such proofs, called the deterministic all-versus-nothing proof and the probabilistic all-versus-nothing proof, are both widely investigated. So far, all previous deterministic all-versus-nothing proofs of Bell nonlocality are constructed based on stabilizer states. To break with this tradition, some deterministic all-versus-nothing proofs induced from non-stabilizer states are firstly presented in this work. These results not only can greatly enrich the family of the demonstration of Bell nonlocality without inequalities, but also may provide us some useful resources in certain quantum information processing.