Secret Key Rate of Quantum Key Distribution Assuming Worst-Case Attacks

Quantum Key Distribution (QKD) represents a revolutionary approach in the field of cryptography, offering the potential for unconditional security by leveraging the principles of quantum mechanics. This paper addresses the crucial issue of calculating secure key rates in entanglement based QKD systems. We present a method of key rate calculations that is independent of an eavesdropper's quantum system, relying solely on the quantum states shared between two communicating parties under the assumption of a worst-case attack. We undertake a comparison of asymptotic key rates with those observed in the finite regime, in which only a limited number of quantum states are exchanged. Furthermore, we investigate the influence of entanglement distillation on the achievable key rates. By identifying the numerically optimal number of entanglement distillation iterations based on the initial fidelity and the number of exchanged quantum states, we demonstrate how to achieve a balance between the quantity and quality of entangled states, thereby maximizing the secure key rate. Our results show that there is a unique optimum within a defined search range. Moreover, we determine the minimum number of exchanged quantum states necessary to attain a positive key rate and to obtain a desired number of secure key bits, which are both contingent upon the quality of the communication channel. It is anticipated that the insights gained from this work will prove instrumental in the development of optimal routing strategies in quantum communication networks.