Security of advanced quantum key distribution protocols in realistic conditions

Quantum key distribution (QKD) allows two users to generate a random secret key, which they can use to securely exchange a message. Unlike many other cryptographic schemes, QKD offers information-theoretical security based on the laws of physics. In recent years, major theoretical and experimental advancements have been made. Among these are two novel protocols, memory-assisted (MA) QKD and twin-field (TF) QKD, which can both improve the secret-key rate scaling with channel length, potentially allowing QKD to be performed at longer distances. The main motivation of this thesis is to incorporate more realistic assumptions into the security proofs and performance analyses of these new protocols. One common assumption made in QKD security proofs is that the protocol is run for an infinitely long time, which allows the users to obtain a perfect statistical characterisation of the quantum channel. In this thesis, we drop this assumption for a TF-QKD variant that is well suited for experimental implementation, proving its security in the finite-key regime. We also analyse the finite-key performance of MA-QKD, concluding that it is particularly resistant to its statistical fluctuation effects. Moreover, we develop an alternative finite-key security analysis approach based on random sampling theory, and apply it to the loss-tolerant protocol, which can ensure security in the presence of flawed sources. Compared to previous finite-key security proofs of the protocol, our analysis offers better performance. Another common assumption is that the users can emit laser pulses with a continuous random phase. In practice, this is difficult to achieve, and the phase is often randomised discretely. In this thesis, we prove the security of a TF-QKD variant that relies on discrete phase randomisation, and show that, using certain post-selection techniques, it can provide higher secret-key rates than an equivalent continuously-randomised protocol.