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

Abstract

The all-versus-nothing proof of Bell nonlocality is a prominent demonstration of Bell’s theorem without inequalities. There are two kinds of such proofs: the deterministic all-versus-nothing proof and the probabilistic all-versus-nothing proof, which have received extensive research attention. Traditionally, all previous deterministic all-versus-nothing proofs are constructed based on stabilizer states. However, this work presents new deterministic proofs derived from non-stabilizer states, thereby breaking away from this conventional approach. These novel results not only significantly broaden the range of demonstrations of Bell nonlocality without inequalities but also offer valuable resources for certain quantum information processing applications.

Keywords

• Bell nonlocality
• deterministic all-versus-nothing proof
• Hardy-like quantum pigeonhole paradox
• non-stabilizer States