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

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 $\sim 66.7\%$ 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.

10 pages, 1 figure, 2 tables

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Cited by in corpus (10)

• Bell inequalities violated using detectors of low efficiency
• Beating detection loophole in nonlinear entanglement witnesses
• Detection loophole in measurement-device-independent entanglement witness
• Closing the detection loophole in multipartite Bell experiments with a limited number of efficient detectors
• Noisy quantum input loophole in measurement-device-independent entanglement witnesses
• Tight detection efficiency bounds of Bell tests in no-signaling theories
• Detection Efficiency Bounds in (Semi-)Device-Independent Scenarios
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses
• Effects of the detection loophole on rival entanglement attestation techniques
• How Likely Are You to Observe Non-locality with Imperfect Detection Efficiency and Random Measurement Settings?