Performance Analysis of MDI-QKD in Thermal-Loss and Phase Noise Channels

Measurement-device-independent quantum key distribution (MDI-QKD), enhances quantum cryptography by mitigating detector-side vulnerabilities. This study analyzes MDI-QKD performance in thermal-loss and phase noise channels, modeled as depolarizing and dephasing channels to capture thermal and phase noise effects. Based on this channel framework, we derive analytical expressions for Bell state measurement probabilities, quantum bit error rates (QBER), and secret key rates (SKR) of MDI-QKD. Our simulations reveal that SKR decreases exponentially with transmission distance, with performance further degraded by increasing thermal noise and phase noise, particularly under high thermal noise conditions. These findings offer insights into enhancing MDI-QKD's noise resilience, supporting secure key generation in practical, noisy environments.