Bell Nonlocality from Wigner Negativity in Qudit Systems

• URL: http://arxiv.org/abs/2405.14367v3
• Date: Thu, 14 Nov 2024 18:15:26 GMT
• Title: Bell Nonlocality from Wigner Negativity in Qudit Systems
• Authors: Uta Isabella Meyer, Ivan Šupić, Damian Markham, Frédéric Grosshans,
• Abstract summary: We show how a bipartite entangled qudit state can serve as a witness for nonlocality when it exhibits Wigner negativity. A specified stabilizer state maximally violates the inequality among all qudit states based on its Wigner negativity.
• Score: 1.2499537119440245
• License:
• Abstract: Nonlocality is an essential concept that distinguishes quantum from classical models and has been extensively studied in systems of qubits. For higher-dimensional systems, certain results for their two-level counterpart, like Bell violations with stabilizer states and Clifford operators, do not generalize. On the other hand, similar to continuous variable systems, Wigner negativity is necessary for nonlocality in qudit systems. We show how a bipartite entangled qudit state can serve as a witness for nonlocality when it exhibits Wigner negativity. Additionally, we propose a new generalization of the CHSH inequality for qudits by inquiring correlations related to the Wigner negativity of stabilizer states under the adjoint action of a generalization of the qubit $\pi/8$-gate. A specified stabilizer state maximally violates the inequality among all qudit states based on its Wigner negativity. The Bell operator not only serves as a measure for the singlet fraction but also quantifies the volume of Wigner negativity. Furthermore, we give deterministic Bell violations, as well as violations with a constant number of measurements, for the Bell state relying on operators innate to higher-dimensional systems than the qudit at hand.

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