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

TL;DR

This paper demonstrates that using the three-qubit W state and specific Bell inequalities, the detection efficiency threshold in tripartite Bell tests can be lowered to around 50%, improving experimental feasibility.

Contribution

It introduces a method to reduce the detection efficiency threshold in tripartite Bell tests using the W state and multiple measurement settings, surpassing previous limits.

Findings

Achieved a detection efficiency threshold of 50.13% with an 8-setting Bell inequality.

Lowered the threshold to 50% using a 4-setting Bell test on generic three-qubit states.

Conjectured that 50% is the fundamental limit for three-qubit Bell tests regardless of measurement settings.

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 $\sim66.7\%$ 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.