We present a measurement-device-independent quantum key distribution (MDI-QKD) using single photons in a linear superposition of three orthogonal time-bin states, for generating the key. The orthogonal states correspond to three distinct paths in the delay line interferometers used by two (trusted) sources. The key information is decoded based on the measurement outcomes obtained by an untrusted third party Charles, who uses a beamsplitter to measure the phase difference between pulses traveling through different paths of the two delay lines. The proposed scheme combines the best of both differential-phase-shift (DPS) QKD and MDI-QKD. It is more robust against phase fluctuations, and also ensures protection against detector side-channel attacks. We prove unconditional security by demonstrating an equivalent protocol involving shared entanglement between the two trusted parties. We show that the secure key rate for our protocol compares well to existing protocols in the asymptotic regime. For the decoy-state variant of our protocol, we evaluate the secure key rate by using a phase-post-selection technique. Finally, we estimate the bit error rate and the phase error rate, in the finite key regime.

我们提出了在三个正交时区的线性叠加中使用单个光子的独立于测量设备的量子密钥分布（MDI-QKD）状态，用于生成密钥。正交状态对应于两个（可信）源所使用的延迟线干涉仪中的三个不同路径。基于不受信任的第三方Charles的测量结果对关键信息进行解码，该第三方使用分束器测量通过两条延迟线的不同路径传播的脉冲之间的相位差。所提出的方案结合了差分相移（DPS）QKD和MDI-QKD的优点。它具有更强的抗相位波动性，还可以防止检测器侧通道受到攻击。通过演示涉及两个受信方之间共享纠缠的等效协议，我们证明了无条件安全性。我们表明，我们的协议的安全密钥率与渐近体制中的现有协议比较好。对于我们协议的诱骗状态变体，我们使用阶段后选择技术评估安全密钥率。最后，我们在有限密钥体制中估计误码率和相位误码率。