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

TL;DR

This paper demonstrates that high-dimensional non-stabilizer qudit states can produce deterministic all-versus-nothing proofs of Bell nonlocality, expanding the understanding beyond qubit systems.

Contribution

It provides the first example of a four-qudit non-stabilizer state inducing a deterministic proof of Bell nonlocality in high dimensions.

Findings

High-dimensional non-stabilizer states can induce nonlocality proofs.

A specific four-qudit non-stabilizer state was constructed.

Deterministic all-versus-nothing proofs are possible beyond qubit systems.

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.