Sending-or-Not-Sending with Independent Lasers: Secure Twin-Field Quantum Key Distribution over 509 km

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.

Figure 1

(a) Schematic of our experimental setup. Alice and Bob use remotely frequency-locked stable continuous wave (CW) lasers as sources. These light sources are then modulated by a phase modulator (PM) and three intensity modulators (IM1, IM2, IM3) for phase randomization, encoding, and decoy intensity modulation. ATT: attenuator; PC: polarization controller; PBS: polarization beam splitter; DWDM: dense-wavelength-division-multiplexer; CIR: circulator; BS: beam splitter; SNSPD: superconducting nanowire single-photon detector. (b) The remote frequency-locking system for Alice and Bob’s light sources. The fiber length is fixed to 500 km for all experimental tests. Bi-EDFA: bidirectional erbium-doped fiber amplifier; BS: beam splitter; AOM: acousto-optic modulator; Bi-EDFA: bidirectional erbium-doped fiber amplifiers; FM: Faraday mirror; PD: photodiode. (c) The time sequence of the basic modulation period. Alice (Bob) sequentially modulates 15 signal pulses, four reference pulses and a vacuum state pulse.

Figure 2

Theoretical and experimental noise rates with different fiber lengths. Alice and Bob are assumed to emit at the working intensity, with 2 MHz reference counts detected. The green curve shows the theoretical simulation. The black stars are the experimental results.

Figure 3

SNS-TF-QKD secure key rates. The green diamond indicates a secure key rate of $R=2.42\times {10}^{-7}$ with $2.05\times {10}^{11}$ total pulses sent and $2.04\times {10}^6$ valid detections over a 350 km standard single mode fiber; the black square indicates a secure key rate of $R=1.03\times {10}^{-7}$ with $3.54\times {10}^{11}$ total pulses sent and $2.55\times {10}^6$ valid detections in the experiment of a 408 km ultralow loss fiber; the red circle indicates the experimental secure key rate over a 509-km ultralow loss fiber. The brown cross indicates the experimental secure key rate of [6], and the blue star point shows the experimental secure key rate of [5]. The red curve shows the simulation result for an ultralow loss fiber length of 509 km with noise probability of $1\times {10}^{-8}$ and an $X$-basis baseline error of 0.04; the black dashed curve shows the absolute key rate limit (PLOB bound [19]) of the repeaterless key rate in ultralow loss fiber; and the red dashed curve illustrates the relative PLOB bound [19] of standard optical fiber.