Twin-Field Quantum Key Distribution without Phase Locking

Twin-field quantum key distribution (TF-QKD) has emerged as a promising solution for practical quantum communication over long-haul fiber. However, previous demonstrations on TF-QKD require the phase locking technique to coherently control the twin light fields, inevitably complicating the system with extra fiber channels and peripheral hardware. Here, we propose and demonstrate an approach to recover the single-photon interference pattern and realize TF-QKD without phase locking. Our approach separates the communication time into reference frames and quantum frames, where the reference frames serve as a flexible scheme for establishing the global phase reference. To do so, we develop a tailored algorithm based on fast Fourier transform to efficiently reconcile the phase reference via data postprocessing. We demonstrate no-phase-locking TF-QKD from short to long distances over standard optical fibers. At 50-km standard fiber, we produce a high secret key rate (SKR) of $1.27\mathrm{Mbit}/\mathrm{s}$, while at 504-km standard fiber, we obtain the repeaterlike key rate scaling with a SKR of 34 times higher than the repeaterless secret key capacity. Our work provides a scalable and practical solution to TF-QKD, thus representing an important step towards its wide applications.

Figure 1

No-phase-locking scheme. The interference pattern is evaluated frequently in the $R$ frame, providing a phase reference for the $Q$ frame. The detection events of $D_0$ ($D_1$) are mapped to the amplitude of $+1$ ($-1$) and the detection probability is related to the interference pattern. Each $R$ frame is used twice for the neighboring $Q$ frames.

Figure 2

Experimental setup. Alice (Bob) send their phase- and intensity-modulated states to Charlie to perform single-photon measurements. $D_{0(1)}$ are used to generate secure keys, while $D_{2(3)}$ are used for delay and polarization compensation. PM, phase modulator; IM, intensity modulator; BS, beamsplitter; VOA, variable optical attenuator; EPC, electrical polarization controller; DWDM, dense wavelength-division multiplexer; PBS, polarization beamsplitter; SNSPD, superconducting nanowire single photon detector; MBC, modulator bias controller.

Figure 3

(a) Measured and simulated interference error rate as a function of $T_R$ from $0.1\mathrm{\mu }\mathrm{s}$ to $50\mathrm{\mu }\mathrm{s}$ with different count rates per detector and $T_Q=1\mathrm{\mu }\mathrm{s}$. The simulated results exclude the estimation error and we used the phase noise result of 380-km fiber spools and the lasers linewidth are 5 kHz with a Lorentzian line shape in the simulation and measurement. (b) Interference error rate as functions of the laser linewidth and $T_R=5\mathrm{\mu }\mathrm{s}$ in which the estimation error is also excluded and the phase noise result of 380-km fiber spools is used as the channel noise.

Figure 4

SKRs at different standard fiber distances. The solid line is the simulated SKRs with different finite sizes and two sets of experimental parameters. The fiber loss coefficient is $0.19\mathrm{dB}/\mathrm{km}$. The solid stars denote the experimental results. The orange dashed line denotes ${\mathrm{SKC}}_0$ [6].