Numerical methods for finite-size key rates with different entropic bounds in quantum key distribution

• Main Author: Chung, Rebecca Ru Byn
• Other Authors: Nelly Ng Huei Ying
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Physics; Quantum key distribution; Numerical methods
• Online Access: https://hdl.handle.net/10356/175673
• Institution: Nanyang Technological University

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.