Minimum detection efficiencies for loophole-free genuine nonlocality tests

The certification of quantum nonlocality, which has immense significance in designing device-independent technologies, confronts severe experimental challenges. Detection loopholes, originating from the unavailability of perfect detectors, are one of the major issues among them. In the present study we focus on the minimum detection efficiency (MDE) required to detect various forms of genuine nonlocality, originating from the type of causal constraints imposed on the involved parties. In this context, we demonstrate that the MDE needed to manifest the recently suggested $T_2$-type nonlocality deviates significantly from perfection. Additionally, we have computed the MDE necessary to manifest Svetlichny's nonlocality, with the state-independent approach markedly reducing the previously established bound. Finally, considering the inevitable existence of noise we demonstrate the robustness of the imperfect detectors to certify $T_2$-type nonlocality.

Figure 1

Noise robust MDE for ${\mathcal{B}}_{T_2}$ nonlocality. (a) $\eta$ vs $\theta$ plot for different $p$. The solid black curve represents MDE, i.e., ${\eta }_{\min }^{{\mathcal{B}}_{T_2}}$. The detector should have detection efficiency within the shaded (color online) region to exhibit $T_2$ nonlocality. (b) Three-parameter plot of $p$ vs $\theta$ vs ${\eta }_{\min }^{{\mathcal{B}}_{T_2}}$. It shows that ${\mathcal{B}}_{T_2}$ is fairly noise-tolerant (up to roughly $1.6\%$). Both figures have been drawn considering the symmetric case, i.e., for ${\eta }_A={\eta }_B={\eta }_C=\eta$.