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Odd-parity error rejection (OPER) can drastically improve the asymptotic keyrate of sending-or-not-sending twin-field (SNS-TF) quantum key distribution(QKD). However, in practice, the finite key effects have to be considered forsecurity. Here, we propose a zigzag approach to verify the phase-flip error ofthe survived bits after OPER. Based on this, we can take all the finite keyeffect efficiently in calculating the non-asymptotic key rate. Numericalsimulation shows that our method here produces the highest key rate over alldistances among all existing methods, improving the key rate by more than$100\%$ to $3000\%$ in comparison with different prior art methods with typicalexperimental setting. Also, we show that with the method here, the SNS-TF QKDcan by far break the the absolute bound of repeater-less key rate with whateverdetection 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 thephase flip error rate, further improving the key rate by more than $20\%$.

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