Measurement-device-independent quantum key distribution (MDIQKD) with the decoy-state method negates security threats of both the imperfect single-photon source and detection losses. Lengthening the distance and improving the key rate of quantum key distribution (QKD) are vital issues in practical applications of QKD. Herein, we report the results of MDIQKD over 404 km of ultralow-loss optical fiber and 311 km of a standard optical fiber while employing an optimized four-intensity decoy-state method. This record-breaking implementation of the MDIQKD method not only provides a new distance record for both MDIQKD and all types of QKD systems but also, more significantly, achieves a distance that the traditional Bennett-Brassard 1984 QKD would not be able to achieve with the same detection devices even with ideal single-photon sources. This work represents a significant step toward proving and developing feasible long-distance QKD.

Quantum key distribution (QKD) aims to generate secure private keys shared by two remote parties. With its security being protected by principles of quantum mechanics, some technology challenges remain towards practical application of QKD. The major one is the distance limit, which is caused by the fact that a quantum signal cannot be amplified while the channel loss is exponential with the distance for photon transmission in optical fiber. Here using the 3-intensity sending-or-not-sending protocol with the actively-odd-parity-pairing method, we demonstrate a fiber-based twin-field QKD over 1002 km. In our experiment, we developed a dual-band phase estimation and ultra-low noise superconducting nanowire single-photon detectors to suppress the system noise to around 0.02 Hz. The secure key rate is $9.53\times {10}^{-12}$ per pulse through 1002 km fiber in the asymptotic regime, and $8.75\times {10}^{-12}$ per pulse at 952 km considering the finite size effect. Our work constitutes a critical step towards the future large-scale quantum network.

Based on the novel idea of twin-field quantum key distribution [TF-QKD; Lucamarini et al., Nature (London) 557, 400 (2018)], we present a protocol named the “sending or not sending TF-QKD” protocol, which can tolerate large misalignment error. A revolutionary theoretical breakthrough in quantum communication, TF-QKD changes the channel-loss dependence of the key rate from linear to square root of channel transmittance. However, it demands the challenging technology of long-distance single-photon interference, and also, as stated in the original paper, the security proof was not finalized there due to the possible effects of the later announced phase information. Here we show by a concrete eavesdropping scheme that the later phase announcement does have important effects and the traditional formulas of the decoy-state method do not apply to the original protocol. We then present our “sending or not sending” protocol. Our protocol does not take postselection for the bits in $Z$-basis (signal pulses), and hence the traditional decoy-state method directly applies and automatically resolves the issue of security proof. Most importantly, our protocol presents a negligibly small error rate in $Z$-basis because it does not request any single-photon interference in this basis. Thus our protocol greatly improves the tolerable threshold of misalignment error in single-photon interference from the original a few percent to more than $45\%$. As shown numerically, our protocol exceeds a secure distance of 700, 600, 500, or 300 km even though the single-photon interference misalignment error rate is as large as $15\%, 25\%, 35\%$, or $45\%$.

Twin-field (TF) quantum key distribution (QKD) promises high key rates over long distances to beat the rate-distance limit. Here, applying the sending-or-not-sending TF QKD protocol, we experimentally demonstrate a secure key distribution that breaks the absolute key-rate limit of repeaterless QKD over a 509-km-long ultralow loss optical fiber. Two independent lasers are used as sources with remote-frequency-locking technique over the 500-km fiber distance. Practical optical fibers are used as the optical path with appropriate noise filtering; and finite-key effects are considered in the key-rate analysis. The secure key rate obtained at 509 km is more than seven times higher than the relative bound of repeaterless QKD for the same detection loss. The achieved secure key rate is also higher than that of a traditional QKD protocol running with a perfect repeaterless QKD device, even for an infinite number of sent pulses. Our result shows that the protocol and technologies applied in this experiment enable TF QKD to achieve a high secure key rate over a long distribution distance, and is therefore practically useful for field implementation of intercity QKD.

The relatively low key rate seems to be the major barrier to its practical use for the decoy-state measurement-device-independent quantum key distribution (MDI-QKD). We present a four-intensity protocol for the decoy-state MDI-QKD that hugely raises the key rate, especially in the case in which the total data size is not large. Also, calculations show that our method makes it possible for secure private communication with fresh keys generated from MDI-QKD with a delay time of only a few seconds.