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 ∼66.7% and 60%, respectively. Using the three-qubit W state and a 3-setting Bell inequality, we beat these thresholds and with an 8-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 4-setting Bell test. We conjecture that the limit of 50% is unbeatable using three-qubit states and any number of measurements.
@article{arxiv.1504.05934,
title = {Closing the detection loophole in tripartite Bell tests using the W state},
author = {Karoly F. Pal and Tamas Vertesi},
journal= {arXiv preprint arXiv:1504.05934},
year = {2015}
}