Breaking the Rate-Loss Bound of Quantum Key Distribution with Asynchronous Two-Photon Interference

Twin-field quantum key distribution can overcome the secret key capacity of repeaterless quantum key distribution via single-photon interference. However, to compensate for the channel fluctuations and lock the laser fluctuations, the techniques of phase tracking and phase locking are indispensable in experiment, which drastically increase experimental complexity and hinder free-space realization. We herein present an asynchronous measurement-device-independent quantum key distribution protocol that can surpass the secret key capacity even without phase tracking and phase locking. Leveraging the concept of time multiplexing, asynchronous two-photon Bell-state measurement is realized by postmatching two interference detection events. For a 1 GHz system, the new protocol reaches a transmission distance of 450 km without phase tracking. After further removing phase locking, our protocol is still capable of breaking the capacity at 270 km. Intriguingly, when using the same experimental techniques, our protocol has a higher key rate than the phase-matching-type twin-field protocol. In the presence of imperfect intensity modulation, it also has a significant advantage in terms of the transmission distance over the sending-or-not-sending-type twin-field protocol. With high key rates and accessible technology, our work provides a promising candidate for practical scalable quantum communication networks.

Popular Summary

Society is inseparable from the services provided by the modern internet, which distributes vast amounts of sensitive digital information. The quantum internet, the next generation of the internet, could revolutionize the way in which information exchange is protected in the future. Establishing a global quantum key distribution (QKD) network connecting fiber channels and free space is the prototype and an important ingredient of the quantum internet. The state-of-art techniques enable a transmission distance over 830 km in the fiber channel with the twin-field QKD protocol at the cost of complicated and expensive experimental techniques, which excludes it from realistic network and free-space deployment.

Here, we propose a novel QKD protocol, “asynchronous measurement-device-independent QKD protocol,” which removes these experimental requirements and has better performance compared with previous twin-field-type protocols in realistic scenarios. Our essential idea is that the two time bins of a phase-encoded qubit can be decoupled. Using time multiplexing, one can establish an asynchronous two-photon Bell state by postmatching two phase-correlated interference events. Using simple experimental setups, our protocol can achieve a key rate of 0.15 Mbit/s at intercity distance, which is sufficient for a variety of tasks, including audio and video encryption.

Our proposal paves the way for an economically large scalable QKD network integrating fiber channels, seawater, and satellite-to-ground data. We anticipate that the key idea of this work, asynchronous two-photon interference, will bring exciting inspiration to other quantum network ingredients, including quantum repeaters and quantum entanglement distribution.

Figure 1

Basic idea of the adaptive MDIQKD scheme [83] and this work. (a) In the adaptive MDIQKD scheme, Alice and Bob send $m$ single-photon pulses to Charlie using spatial multiplexing. Charlie applies quantum nondemolition (QND) measurement to confirm the arrival of pulses, matches the arriving pulses using optical switches (SWs), and performs two-photon Bell measurements (BMs) on the pairs. (b) In our asynchronous-MDIQKD protocol, Alice and Bob send $N$ pulses to Charlie to perform single-photon interference (SPI), and a two-photon Bell state is obtained by postmatching two successful SPI events.

Figure 2

Schematic of case 1 and case 2. Each time bin is represented by a lattice, and detection events are painted in deep purple. Case 1: a detection event around which other detection events can be found within $T_c$; case 2: a detection event around which there are no other detection events within $T_c$. Here $N_T$ is the total number of pulses sent within $T_c$, which is proportional to the system repetition rate.

Figure 3

Schematic of the setup for the asynchronous-MDIQKD protocol. Alice and Bob utilize a narrow-linewidth continuous-wave laser, intensity modulator (IM), phase modulator (PM), and attenuator (ATT) to prepare phase-randomized weak coherent pulses with different intensities and phases. Charlie performs interference measurement with a beam splitter (BS) and single-photon detectors. Charlie announces the detection events where only the detector $\mathbf{L}$ or $\mathbf{R}$ clicks.

Figure 4

HOM visibility and the error rate as a function of the frequency difference between two lasers $\delta v$. We set the time interval of two consecutive time bins $\tau =1\mu \mathrm{s}$. The blue line is the HOM visibility, and the orange dotted line is the interference error rate.

Figure 5

Test results of the frequency difference between two independent lasers, which are obtained by manually adjusting the temperature. (a) Frequency difference between two NKT lasers for 60 s. (b) Histogram of the frequency difference distribution between two NKT lasers. The mean frequency difference is 145 kHz. (c) Frequency difference between two RIO Orion lasers of 60 s. (d) Histogram of the frequency difference distribution between two RIO Orion lasers, where the mean value is 92.5 kHz. Note that, if using automatic feedback systems, the frequency difference can be further reduced.

Figure 6

The bit error rate in the $X$ basis as a function of the matching time interval $T_c$, where both phase tracking and phase locking are not adopted. The distance between Alice and Bob is 300 km and the system repetition rate is $F=4$ GHz. The frequency difference $\delta v$ is set to 10, 50, and 100 kHz.

Figure 7

Secret key rates of the asynchronous MDIQKD with short time matching as a function of the distance when implemented without phase tracking. Here, we set the matching time interval $T_c=50\mu \mathrm{s}$, the system repetition rate is $F=1$ GHz, and the angle of misalignment in the $X$ basis $\sigma =\pi /10$. Our protocol can break the PLOB bound at a distance of approximately 280 km with $N={10}^{12}$, and the transmission distance reaches 450 km.

Figure 8

Secret key rates of our protocol with short-term matching as a function of the distance where both phase tracking and phase locking are not adopted. Different system repetition rates $F$, matching time intervals $T_c$, and frequency differences $\delta v$ are taken into consideration. Red line denotes $F=10$ GHz, $T_c=1\mu \mathrm{s}$, $\delta v=100$ kHz; blue line denotes $F=4$ GHz, $T_c=10\mu \mathrm{s}$, $\delta v=10$ kHz; yellow line denotes $F=1$ GHz, $T_c=20\mu \mathrm{s}$, $\delta v=3$ kHz. Our protocol can overcome the PLOB bound at 270 km with a key rate of $2\times {10}^{-5}$.

Figure 9

Comparison of the secret key rates of the asynchronous MDIQKD with arbitrary time matching, PMQKD [40] and AOPP [81] in symmetric channels. The numerical results here show that our protocol has a notable advantage and is able to achieve a long transmission distance of 620 km.

Figure 10

Comparison of secret key rates of our protocol with arbitrary time matching, PMQKD, and AOPP versus transmission distance in asymmetric channels. Our protocol exhibits a decent performance in asymmetric channels.