Switching in quantum networks: an optimization investigation

Quantum key distribution (QKD) promises information theoretic security. However, the distances over which complete security can be achieved are fundamentally limited in the absence of quantum repeaters. Thus, a key question is how to build a quantum network (QN) given this restriction. One paradigm that has been considered is trusted node (TN) quantum networks where intermediate trusted nodes are used as relays of quantum keys. Another paradigm is to route key channels through intermediate nodes optically, either through wavelength or fiber switching, thus avoiding the use of TNs. In both of these paradigms, a QKD receiver or transmitter at a specific node can be shared between multiple QKD transmitters or receivers at different nodes in order to reduce the overall costs; this sharing can be enabled via an optical switch. In this paper, we investigate the two paradigms for designing QNs. In the TN model we assume the Decoy BB84 protocol, whereas in the non-TN model, we employ twin-field QKD (TF-QKD) due to the increased single hop distances. We present mixed integer linear program models to optimize network design in both of these paradigms and use these to investigate the viability of switching in the network models as a method of sharing devices. We show that sharing of devices can provide cost reduction in QNs up to a certain transmission requirement rate between users in the TN model, while also providing benefits even at significantly higher transmission requirements in the TF-QKD model. The specific value of this rate is dependent on the network graph; however, for mesh topology TN networks this is expected to occur at average key transmission requirements of
${\sim}1000 {-} 5000\;{\rm bits/s}$
. We further use the models to investigate the effects of different network parameters, such as cooling costs, switch frequency, and device costs. We show that cooled detectors are useful in large TF-QKD networks, despite higher costs, but are only useful in TN networks when transmission requirements are very high or cooling is cheap. We also investigate how network costs vary with switching frequency and switch loss, showing that compromising for slightly faster switching times and higher loss switches does not significantly increase network costs; thus a significant effort in improving switch loss may not be necessary. Finally, we look at how the benefits of sharing devices change as the cost of devices changes, showing that for any non-negligible device cost, device sharing is always beneficial at low transmission requirements.