# Zigzag approach to higher key rate of sending-or-not-sending twin field quantum key distribution with finite key effects

## TL;DR

This paper introduces a zigzag approach for SNS-TF quantum key distribution that effectively accounts for finite key effects, significantly boosting key rates and surpassing existing bounds in practical scenarios.

## Contribution

The paper proposes a novel zigzag method to verify phase-flip errors and incorporate finite key effects, achieving unprecedented key rates in SNS-TF QKD.

## Key findings

- Achieves 100% to 3000% higher key rate compared to prior methods.
- Breaks the absolute bound of repeater-less key rate across all distances.
- Reaches a non-asymptotic key rate over 40 times the practical bound with 10^12 pulses.

## Abstract

Odd-parity error rejection (OPER) can drastically improve the asymptotic key rate of sending-or-not-sending twin-field (SNS-TF) quantum key distribution (QKD). However, in practice, the finite key effects have to be considered for security. Here, we propose a zigzag approach to verify the phase-flip error of the survived bits after OPER. Based on this, we can take all the finite key effect efficiently in calculating the non-asymptotic key rate. Numerical simulation shows that our method here produces the highest key rate over all distances among all existing methods, improving the key rate by more than $100\%$ to $3000\%$ in comparison with different prior art methods with typical experimental setting. Also, we show that with the method here, the SNS-TF QKD can by far break the the absolute bound of repeater-less key rate with whatever detection efficiency. We can even reach a non-asymptotic key rate more than $40$ times of the practical bound and $13$ times of the absolute bound with $10^{12}$ pulses. Besides, we apply the McDiarmid inequality to estimate the phase flip error rate, further improving the key rate by more than $20\%$.