We address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $\eta$ that must be surpassed to avoid the detection loophole. Here, we propose a general method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. This is accomplished by entangling two particles in $N$ orthogonal subspaces (e.g., $N$ degrees of freedom) and conducting $N$ Bell tests in parallel. Furthermore, the proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities, for which the so-called simultaneous measurement loophole is closed, and the maximum value for local hidden-variable theories is simply the $N$th power of the one of the Bell inequality initially considered. We show that, for the PNP Bell inequalities, the critical detection efficiency decays exponentially with $N$. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality.

中文翻译：

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任何贝尔不等式的临界检测效率呈指数下降

我们解决了关闭贝尔实验中检测效率漏洞的问题，这对于实际应用至关重要。每个贝尔不等式都有一个临界检测效率$\eta$必须超越，以避免检测漏洞。在这里，我们提出了一种通用方法，用于将任何贝尔不等式的临界检测效率降低到任意低值。这是通过将两个粒子纠缠在$否$正交子空间（例如，$否$自由度）和进行$否$贝尔并行测试。此外，所提出的方法是基于引入惩罚$否$-product (PNP) Bell 不等式，所谓的同时测量漏洞被关闭，局部隐变量理论的最大值就是$否$最初考虑的贝尔不等式之一的 th 次方。我们表明，对于 PNP 贝尔不等式，临界检测效率随指数衰减$否$. 我们的方法的优势通过对由 Clauser-Horne-Shimony-Holt 不等式产生的 PNP 贝尔不等式的详细研究来说明。