The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.

Clauser-Horne-Shimony-Holt (CHSH) 不等式检验被广泛用作使局部确定性理论无效的手段。大多数通过实验测试非定域性的尝试都假设了在实际实验中不成立的非物理理想化，即无噪声测量。我们证明了对 CHSH 不等式的实验违反，该不等式没有理想化，并以高置信度排除了局部模型。我们表明，对于测量的任何非零噪声参数，总是可以违反 CHSH 不等式。有趣的是，在带有噪声测量的 CHSH 测试中，较少的纠缠表现出更多的非局域性。此外，我们从理论上提出并通过实验证明了如何使用带有噪声测量的 CHSH 测试来检测两个量子位状态上的弱纠缠。