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Recently, a kind of deterministic all-versus-nothing proof of Bellnonlocality induced from the qubit non-stabilizer state was proposed, breakingthe tradition that deterministic all-versus-nothing proofs are always derivedfrom 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 reducedto the qubit version. So far, whether high dimensional non-stabilizer statescan induce nontrivial deterministic all-versus-nothing proofs of Bellnonlocality remains unknown. Here we present an example induced from a specificfour-qudit non-stabilizer state (with d = 4), showing that such proofs can beconstructed in high dimensional scenarios as well.

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