Reconciliation for Satellite-Based Quantum Key Distribution

This thesis reports on reconciliation schemes based on Low-Density Parity-Check (LDPC) codes in Quantum Key Distribution (QKD) protocols. It particularly focuses on a trade-off between the complexity of such reconciliation schemes and the QKD key growth, a trade-off that is critical to QKD system deployments. A key outcome of the thesis is a design of optimised schemes that maximise the QKD key growth based on finite-size keys for a range of QKD protocols. Beyond this design, the other four main contributions of the thesis are summarised as follows. First, I show that standardised short-length LDPC codes can be used for a special Discrete Variable QKD (DV-QKD) protocol and highlight the trade-off between the secret key throughput and the communication latency in space-based implementations. Second, I compare the decoding time and secret key rate performances between typical LDPC-based rate-adaptive and non-adaptive schemes for different channel conditions and show that the design of Mother codes for the rate-adaptive schemes is critical but remains an open question. Third, I demonstrate a novel design strategy that minimises the probability of the reconciliation process being the bottleneck of the overall DV-QKD system whilst achieving a target QKD rate (in bits per second) with a target ceiling on the failure probability with customised LDPC codes. Fourth, in the context of Continuous Variable QKD (CV-QKD), I construct an in-depth optimisation analysis taking both the security and the reconciliation complexity into account. The outcome of the last contribution leads to a reconciliation scheme delivering the highest secret key rate for a given processor speed which allows for the optimal solution to CV-QKD reconciliation