The trade-off between distance and secret key generation rate remains one of the major challenges in the practical implementation of quantum key distribution (QKD). As a solution, a twin field QKD protocol was proposed by Lucamarini et al (2018) to address this challenge. In this protocol, the achievable secret key rate scales with the square root of channel transmittance and can surpass the secret key capacity for repeaterless QKD. However, the protocol exploits phase to encode information which presents the problem of active stabilization of interferometers. We propose a reference frame independent twin field quantum key distribution (RFITF QKD), which does not require the reference frames’ alignment. Thus, this reduces the complexity of practical QKD systems in achieving active stabilization of phase. Moreover, we employ the loss-tolerant method proposed by Tamaki et al (2014) which allows us to prove the security of the protocol by considering imperfections in the state preparation. Our simulation results show that our proposed protocol can extract a secure key over a transmission distance of l = 505 km, l = 516 km and l = 530 km for deviation of 8.42, 7.28 and 5.15, respectively from the desired phase encoding angle. These results demonstrate that despite the state preparation flaws, the key rates achieved are still comparable to the perfect encoding scenario. When our proposed protocol is implemented with an imperfect source, it achieves a transmission distance beyond the secret key capacity bound for repeaterless QKD.

距离和密钥生成率之间的权衡仍然是量子密钥分发 (QKD) 实际实现中的主要挑战之一。作为解决方案，Lucamarini等人提出了双场 QKD 协议(2018) 来应对这一挑战。在该协议中，可实现的密钥速率与信道传输率的平方根成比例，并且可以超过无中继器 QKD 的密钥容量。然而，该协议利用相位来编码信息，这提出了干涉仪主动稳定的问题。我们提出了一种独立于参考系的双场量子密钥分配（RFITF QKD），它不需要参考系的对齐。因此，这降低了实际 QKD 系统在实现相位主动稳定方面的复杂性。此外，我们采用了 Tamaki等人提出的容错方法(2014) 允许我们通过考虑状态准备中的缺陷来证明协议的安全性。我们的仿真结果表明，我们提出的协议可以在l = 505 km、l = 516 km 和l = 530 km的传输距离内提取安全密钥，分别与所需的相位编码角度偏差为 8.42、7.28 和 5.15。这些结果表明，尽管存在状态准备缺陷，但实现的关键速率仍可与完美编码方案相媲美。当我们提出的协议在不完善的源下实现时，它实现的传输距离超出了无中继器 QKD 的密钥容量限制。