Sebastiaan Brand

The fundamental distance limit for quantum key distribution due to photon loss can be overcome by intermediate nodes called quantum repeaters. We provide analytical bounds on the mean and quantiles of the entanglement delivery time for a very general class of repeater schemes, which significantly improve upon existing work. Our bounds enable the analytical assessment of repeater in the presence of time-dependent noise, such as imperfect memories, and are useful for the design and analysis of network sizes beyond the reach of numerics.

Losses in the physical transmission medium fundamentally limit the distance that quantum key distribution schemes can cover. By means of quantum repeaters, the reach of these schemes can be extended and chains of quantum repeaters could in principle cover arbitrarily long distances. Here, we first provide an efficient algorithm for completely characterizing the behaviour of a large class of repeater chain protocols. The algorithm determines the fidelity and generation time (waiting time) of the first generated entangled pair between the end nodes of a quantum repeater chain. It has polynomial runtime in the size of the support of the waiting time probability distribution. This runtime improves upon the exponential runtime of existing algorithms and allows us to analyze repeater chains of thousands of segments for some parameter regimes. Second, we use the algorithm for optimizing the achievable secret key rate. For this, we consider a family of repeater schemes generalizing the BDCZ scheme. In particular, the schemes incorporate a cut-off condition that enables to mitigate the effects of decoherence. We find that the use of the optimal cut-off extends the parameter regime for which secret key can be generated and moreover significantly increases the secret-key rate for a large range of parameters. Our algorithms thus serve as useful tools for the design and realization of long-distance quantum key distribution networks.