By Ghalaii M, Papanastasiou P, Pirandola S.
Submitted to arXiv on 22 March 2022.
Gaussian networks are fundamental objects in network information theory. Here many senders and receivers are connected by physically motivated Gaussian channels while auxiliary Gaussian components, such as Gaussian relays, are entailed. Whilst the theoretical backbone of classical Gaussian networks is well established, the quantum analogue is yet immature. Here, we theoretically tackle composable security of arbitrary Gaussian quantum networks (quantum networks), with generally untrusted nodes, in the finite-size regime and put forward a general methodology for parameter estimation, which is only based on the data shared by the remote end-users. Taking a chain of quantum repeaters as an example, we find that the composable key rate of the chain can beat the fundamental repeaterless limit with practical block sizes.