Asymmetric Sending-or-Not-Sending Twin-Field Quantum Key Distribution

We propose an improved protocol that combines the code-bit option [z] of the Universal SNS framework with asymmetric sending probabilities across odd-indexed and even-indexed time windows. This approach increases the fraction of single-sided events that contribute to the raw key, while the [z] option ensures that all heralded events involving the signal and vacuum intensities are retained as code bits. Numerical simulations demonstrate that the proposed protocol significantly outperforms both the SNS protocol with actively odd-parity pairing (SNS-AOPP) and the Universal SNS protocol with the [x, y, z] option. At a secret key rate of 1 kbps, the proposed protocol extends the maximum secure distance by 103.7 km compared to SNS-AOPP. The key rate improvement reaches more than a factor of 11 over the entire distance range, and this result shows that the combination of the [z] option with asymmetric sending probabilities provides a simple yet effective means of enhancing the performance of SNS-TF-QKD without requiring changes to the quantum hardware.