Tristan Le Roy-Deloison

Losses in the transmission channel, which increase with distance, pose a major obstacle to photonics demonstrations of quantum nonlocality and its applications to device-independent protocols such as device-independent quantum key distribution. Recently, Chaturvedi, Viola, and Pawlowski (CVP) arXiv:2211.14231 introduced a variation of standard Bell experiments, which we call routed Bell experiments, with the goal of extending the range over which quantum nonlocality can be demonstrated. In these experiments, in some of the rounds, photons from the source are routed by an actively controlled switch to a nearby test device instead of the distant one. CVP showed that there are quantum correlations in routed Bell experiments such that the outcomes of the remote device cannot be classically predetermined, even when its detection efficiency is arbitrarily low. In our work, we show that the correlations considered by CVP, though they cannot be classically predetermined, do not require the transmission of quantum systems to the remote device. This leads us to properly define the concept of 'short-range' and 'long-range' quantum correlations in routed Bell experiments. We then explore the conditions under which short-range quantum correlations can be ruled out. We find that routed Bell experiments do allow for reducing the detection efficiency threshold but the improvements are smaller than those suggested by CVP's analysis. We then investigate DIQKD protocols based on the routed setup. We show how to analyze the security of these protocols and compute lower bounds on the key rates using non-commutative 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. We find that in an ideal case routed DIQKD protocols can significantly improve detection efficiency requirements, by up to 30%, compared to their non-routed counterparts. Notably, the routed BB84 protocol achieves a positive key rate with a detection efficiency as low as 50% for the distant device, the minimal threshold for any DIQKD 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.