Improved Nonlocality Certification via Bouncing between Bell Operators and Inequalities

TL;DR

This paper introduces an optimization approach that enhances Bell nonlocality certification by mapping between Bell inequalities and Hamiltonians, leading to more robust detection methods applicable to large quantum systems.

Contribution

It develops a novel optimization scheme for improving nonlocality certification through flexible mappings between Bell inequalities and Hamiltonians, enhancing robustness and experimental feasibility.

Findings

Mapped Hamiltonian models to new inequalities with better classical bounds

Maximized quantum violations considering experimental imperfections

Successfully applied to a 70-qubit superconducting system

Abstract

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be certified via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here, we present an optimization scheme to improve nonlocality certification by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds than the original one, enabling a more robust detection of nonlocality. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical demonstration, we apply this method to an XXZ-like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, as well as combining the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient nonlocality certification techniques and enable broader experimental explorations.