We study the problem of closing the detection loophole in three-qubit Bell tests, the experimentally most relevant case beyond the usual bipartite scenario, and show that the minimal detection efficiencies required can be considerably lowered compared to the two-qubit case. The lowest reported detection efficiency thresholds for two and three qubits so far are $\sim 66.7$ and $60\%$, respectively. Using the three-qubit $W$ state and a three-setting Bell inequality, we beat these thresholds and with an eight-setting Bell inequality we reach $50.13\%$. We also investigate generic three-qubit states which allow us to attain a detection efficiency of $50\%$ in a four-setting Bell test. We conjecture that the limit of $50\%$ is unbeatable using three-qubit states and any number of measurements.

• Received 27 April 2015

DOI:https://doi.org/10.1103/PhysRevA.92.022103