Device-Independent Quantum Key Distribution Based on Routed Bell Tests

Photon losses are the main obstacle to fully photonic implementations of device-independent quantum key distribution (DIQKD). Motivated by recent work showing that routed Bell scenarios offer increased robustness to detection inefficiencies for the certification of long-range quantum correlations, we investigate DIQKD protocols based on a routed setup. In these protocols, in some of the test rounds, photons from the source are routed by an actively controlled switch to a nearby test device instead of the distant one. We show how to analyze the security of these protocols and compute lower bounds on the key rates using noncommutative polynomial optimization and the Brown-Fawzi-Fawzi method. We determine lower bounds on the asymptotic key rates of several simple two-qubit routed DIQKD protocols based on CHSH or BB84 correlations and compare their performance to standard protocols. For high-quality short-path tests, we find that routed DIQKD protocols are significantly more robust to losses, showing an improvement of approximately <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mn>30</a:mn><a:mi mathvariant="normal">%</a:mi></a:math> in the detection efficiency compared to their nonrouted counterparts. This translates to a large improvement in the distance over which nonzero key can be distilled in optical setups with near-perfect single-photon detectors, where the main source of loss in the setup is due to transmission in the fiber. Notably, the routed BB84 protocol achieves a positive key rate with a detection efficiency as low as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><e:mn>50</e:mn><e:mi mathvariant="normal">%</e:mi></e:math> for the distant device, the minimal threshold for any QKD protocol featuring two untrusted measurements. However, the advantages we find are highly sensitive to noise and losses affecting the short-range correlations involving the additional test device.