Tight detection efficiency bounds of Bell tests in no-signaling theories

Abstract: No-signaling theories, which can contain nonlocal correlations stronger than classical correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In principle, the nonlocality of these theories can be verified via Bell tests. In practice, however, inefficient detectors may make Bell tests unreliable, which is called the detection efficiency loophole. In this work, we show almost tight lower and upper bounds of the detector efficiency requirement for demonstrating the nonlocality of no-signaling theories, by designing a general class of Bell tests. In particular, we show tight bounds for two scenarios: the bipartite case and the multipartite case with a large number of parties. To some extent, these tight efficiency bounds quantify the nonlocality of no-signaling theories. Furthermore, our result shows that the detector efficiency can be arbitrarily low even for Bell tests with two parties, by increasing the number of measurement settings. Our work also sheds light on the detector efficiency requirement for showing the nonlocality of the quantum theory.