Finite Size of Gaussian-Modulated Continuous-Variable Quantum Key Distribution with an Untrusted Entanglement Source

The Gaussian-modulated continuous-variable quantum key distribution (GMCVQKD) scheme based on untrusted entanglement sources simulates scenarios where the source may be controlled by an attacker. However, Existing analyses often assume ideal settings and overlook finite-size effects. This paper addresses these gaps by evaluating the GMCVQKD scheme under specific attack scenarios, considering limited signal exchanges between Alice and Bob. We examine the secret key rate under finite-size conditions, analyzing factors such as the positioning of the entanglement source and the effectiveness of the reconciliation process., and compares results to the asymptotic regime. The findings reveal a decline in key rate under finite-size effects, highlighting the influence of statistical fluctuations. This work advances practical CVQKD implementation and offers theoretical guidance for system deployment.