Ahmed Q. Lawey

We present a unified analytical framework for mode‑pairing quantum key distribution (MP QKD) that incorporates both discrete phase randomisation and finite‑size statistical fluctuations. By mapping MP QKD to an equivalent two‑mode measurement-device-independent QKD, we derive closed‑form bounds for key‑rate estimation without numerical optimisation. Using Chernoff bounds, we evaluate realistic system performance and show how the interplay between phase‑slice number and block size impacts whether the protocol can surpass the PLOB bound. The results highlight the practicality of our approach for real‑time evaluation and implementation of DPR MP QKD in a finite-key setting.

We consider discrete phase randomisation (DPR) for several quantum key distribution (QKD) protocols. Full continuous phase randomisation of weak laser pulses (WCPs) would create an output state that is diagonal in Fock basis. This will simplify the security proof of QKD protocols that rely on WCPs or decoy states. In practice, however, such an ideal phase randomisation may not be achievable. Instead, we may actively choose a discrete number of global phase values for our WCPs. The security proof with DPR has been reported for several QKD protocols, which often requires numerical optimisation. In this work, we develop analytical bounds on the secret key generation rate for BB84 and measurement-device-independent (MDI) QKD protocols with DPR. These analytical bounds closely match the numerical results. We then extend our results to the newly proposed mode-pairing (MP) QKD protocols, which offer favourable rate-versus-distance scaling, with DPR. We show that the number of phase slices needed for MP-QKD to approach the ideal case is larger than that of MDI-QKD.

Quantum data centres (QDCs) are a promising way of scaling up quantum computers. In a single-processor quantum computer, the number of high-quality computational qubits is limited by cross talk and difficulties in addressing individual qubits when many qubits share the same housing. QDCs circumvent these challenges by linking together multiple small quantum processing units (QPUs) over short distances. With this architecture, the intra-QPU noise is kept small, but additional noise is introduced due to the latency of and imperfections in the inter-QPU links. Understanding the trade-offs between these different types of noise is essential for guiding future efforts in QDC manufacture and compilation. We develop and use a classical simulator to emulate the execution of different quantum circuits on an imperfect QDC. An individual inter-QPU CNOT gate is first-considered and then a selection of larger circuits are investigated. In both cases, we implement inter-QPU gates using cat-comm and three variants of TP-comm, which we call 1TP-comm, 2TP-comm and TP-safe, respectively. We find that 1TP-comm and cat-comm yield different output fidelities despite both schemes having the same number of gates, measurements and inter-QPU entanglements. We also determine the relative impacts of entanglement error, intra-QPU gate error and memory depolarisation.