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 $20\%$.

中文翻译：

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具有有限密钥效应的发送或不发送双场量子密钥分配的更高密钥率的锯齿形方法

奇偶校验错误拒绝（OPER）可以显着提高发送或不发送双场（SNS-TF）量子密钥分发（QKD）的渐近密钥率。然而，在实践中，为了安全，必须考虑有限的密钥效应。在这里，我们提出了一种锯齿形方法来验证 OPER 后幸存位的相位翻转误差。在此基础上，我们可以在计算非渐近键率时有效地考虑所有有限键效应。数值模拟表明，在所有现有方法中，我们的方法在所有距离上产生最高的关键率，与具有典型实验设置的不同现有技术方法相比，关键率提高了 100% 至 3000 美元。此外，我们展示了使用这里的方法，无论检测效率如何，SNS-TF QKD 都可以打破无中继器密钥率的绝对界限。我们甚至可以通过 10 美元 ^{12}$ 脉冲达到实际界限的 40 美元以上和绝对界限的 13 美元以上的非渐近密钥率。此外，我们应用 McDiarmid 不等式来估计相位翻转错误率，进一步将关键率提高了 20\%$ 以上。