Security-rate trade-off in quantum key distribution: From individual links to large-scale networks

We explore the interplay between security and key rate of a quantum key distribution (QKD) protocol. This fundamental trade-off is investigated both at the link layer, i.e., for a QKD protocol implemented on a channel, and at the network layer, i.e., within the context of a multiuser multihop communication network. In the former scenario, we consider both discrete- and continuous-variable protocols in the composable finite-size framework, showing how their epsilon security restricts the key rate achievable on a single fiber link under various assumptions for the process of parameter estimation. In the latter scenario, we analyze the impact of composable security in the network setting, studying the interplay between end-to-end (ETE) epsilon security and ETE key rate for arbitrarily chosen remote end points. Starting from basic topologies to more complex ones, such as perturbed lattices, we analyze this trade-off under different types of routing strategies. In multipath routing, a greater number of paths can improve key rates, but this enhancement is accompanied by a reduction in the ETE security level. In the setting of single-path routing, we introduce a modified Dijkstra algorithm, which we call “lambda protocol,” able to optimize route construction depending on the joint ETE demand for security and rate. Our results are first derived for specific network instances (i.e., fixed topologies within a given network class) and subsequently extended to ensemble averages over entire network classes, where phase transitions are revealed with respect to node connectivity.