Deterministic All-versus-nothing Proofs of Bell Nonlocality Induced from Qudit Non-stabilizer States

Abstract: Recently, a kind of deterministic all-versus-nothing proof of Bell nonlocality induced from the qubit non-stabilizer state was proposed, breaking the tradition that deterministic all-versus-nothing proofs are always derived from stabilizer states. A trivial generalization to the qudit (d is even) version is by using a special basis map, but such a proof can still be reduced to the qubit version. So far, whether high dimensional non-stabilizer states can induce nontrivial deterministic all-versus-nothing proofs of Bell nonlocality remains unknown. Here we present an example induced from a specific four-qudit non-stabilizer state (with d = 4), showing that such proofs can be constructed in high dimensional scenarios as well.