Closing the detection loophole in tripartite Bell tests using the W state

Pál, Károly Ferenc and Vértesi, Tamás (2015) Closing the detection loophole in tripartite Bell tests using the W state. PHYSICAL REVIEW A, 92 (2). ISSN 2469-9926

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Abstract

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,

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