Experimental Twin-Field Quantum Key Distribution through Sending or Not Sending

Channel loss seems to be the most severe limitation on the practical application of long distance quantum key distribution. The idea of twin-field quantum key distribution can improve the key rate from the linear scale of channel loss in the traditional decoy-state method to the square root scale of the channel transmittance. However, the technical demands are rather tough because they require single photon level interference of two remote independent lasers. Here, we adopt the technology developed in the frequency and time transfer to lock two independent laser wavelengths and utilize additional phase reference light to estimate and compensate the fiber fluctuation. Further, with a single photon detector with a high detection rate, we demonstrate twin field quantum key distribution through the sending-or-not-sending protocol with a realistic phase drift over 300 km optical fiber spools. We calculate the secure key rates with the finite size effect. The secure key rate at 300 km ($1.96\times {10}^{-6}$) is higher than that of the repeaterless secret key capacity ($8.64\times {10}^{-7}$).

Figure 1

Schematics for three different protocols. (a) Decoy-state MDIQKD, where coherent-state pulse pairs in BB84 encoding are sent out and effective events are heralded by twofold clicking. The key rate scales linearly with the channel transmittance. (b) The original decoy state TFQKD [11], where twin fields of coherent states with random phase shifts are sent out in the $X$ and $Y$ bases, and the effective events are heralded by single clicking. The key rate scales with the square root of the channel transmittance. Single-photon interference from remote independent sources are needed for both bases. There can be misalignment errors in both bases and the post announced phase-shift information renders the decoy-state method invalid. (c) Decoy-state SNSTFQKD [21]. In the $Z$ basis, each side independently decides sending with a small probability. The events that one side decides sending, the other side decides not sending, and one and only one detector clicks (as shown in the figure) are the target events to generate secure keys. It is fault tolerant to a large misalignment error in the $X$ basis because there is no misalignment error in the $Z$ basis. The traditional decoy-state method holds because the phase-shift information in the $Z$ basis is never announced. The heralding of a single clicking makes the effective events in the $Z$ basis, and the key rate is in the scale of square root of the channel transmittance. WCS: weak coherent source.

Figure 2

(a) Schematic of our experimental setup. Alice and Bob use frequency-locked continuous-wave (cw) lasers as sources. These lasers are then modulated by a phase modulator (PM) and three amplitude modulators (AMs) for phase randomization, encoding, and decoy intensity modulation. The pulses are then attenuated by an attenuator (ATT) and sent out via fiber spools to Charlie. At Charlie’s measurement station, the pulses from Alice and Bob pass through polarization controllers (PCs) and polarization beam splitters (PBSs), then interfere at a beam splitter (BS). Finally, the light is measured by superconducting nanowire single-photon detectors (SNSPDs). (b) Frequency-locking system for Alice’s and Bob’s lasers. The fiber length between Alice and Bob is set to be the same as the total length of the signal fiber. AOM: acousto-optic modulator, FM: Faraday mirror, PD: photodiode. QWP: Quarter-Wave Plate.

Figure 3

Secure key rates and SNSTFQKD simulation results. The triangles show the experimental results for the first experimental test while the solid green curve represents the simulation results with a dark count probability of around ${10}^{-6}$ and $X$-basis baseline error of approximately 10%. For comparison, the dotted blue curve gives the result of simulating the four-intensity decoy-state MDIQKD protocol [16] with the same parameters but with 2% optical errors in the $X$ basis. The circles show the experimental results for the second test while the solid blue curve represents the simulation with a dark count probability of around ${10}^{-7}$ and $X$-basis baseline error of approximately 2%. The total pulses sent by Alice and Bob for all the experimental tests are $7.2\times {10}^{11}$. The dotted-dashed red curve further assumes a total of $10^{14}$ pulses sent by Alice and Bob with 2% $X$-basis baseline error. Finally, the solid magenta line illustrates the PLOB bound [20].