Numerical methods for finite-size key rates with different entropic bounds in quantum key distribution - Chung, Rebecca Ru Byn (Nanyang Technological University, 2024)
Quantum Key Distribution (QKD) is an important branch of quantum communication in the past few decades due to its security against quantum attacks. As a result, QKD has seen tremendous growth in terms of industrial implementation. Therefore, there exists a need for a reliable numerical method which computes the key rates for a practical QKD setup, taking into account finite-size effects. Various numerical methods have since been proposed for the computation of finite-size key rates using Semi-Definite Programming (SDP). In this thesis, we provided a systematic evaluation of the numerical methods by Winick et al., George et al. and Bunandar et al. for finite-size and device-dependent protocols under i.i.d. collective attack. Through our evaluation, we provided a critical examination of the strengths and weaknesses of these methods. Following the ideas of Dupuis, we also formulated a generalized alpha-Renyi entropic bound on the secret key rate under i.i.d. collective attack, and showed regions of improvement from the conventional approach of using the smooth min-entropy. In particular, we proposed a generalized optimization method for the Renyi entropy for alpha = (1,2] and the min-entropy by adapting from Winick et al.'s method. We then showed that the Renyi entropy indeed gives a tighter bound on the low-signal regime (N~10^5), and outperforms the bound using the von Neumann entropy in regimes of long channel distances and low signal number, thus paving the way for a better understanding of long-distance satellite-based QKD protocols in the presence of finite resources.