It has been debated whether protective measurement implies the reality of the wave function. In this article, I present a new analysis of the relationship between protective measurements and the reality of the wave function. First, I briefly introduce protective measurements and the ontological models framework for them. Second, I give a simple proof of Hardy’s theorem in terms of protective measurements. Third, I analyse two suggested ψ-epistemic models of a protective measurement. It is shown that although these models can explain the appearance of expectation values of observables in a single measurement, their predictions about the variance of the result of a non-ideal protective measurement are different from those of quantum mechanics. Finally, I argue that under an auxiliary finiteness assumption about the dynamics of the ontic state, protective measurement implies the reality of the wave function in the ontological models framework.

中文翻译：

---

保护性测量和波函数的真实性

保护性测量是否意味着波函数的真实性一直存在争议。在本文中，我对保护性测量与波函数的真实性之间的关系进行了新的分析。首先，我简要介绍了保护度量和它们的本体模型框架。其次，我根据保护性测量给出了哈代定理的一个简单证明。第三，我分析了两个建议的保护性测量的 ψ-认知模型。结果表明，虽然这些模型可以解释单次测量中可观测量的期望值的出现，但它们对非理想保护测量结果方差的预测与量子力学不同。最后，我认为在关于本体状态动力学的辅助有限性假设下，