Twin field quantum key distribution promises high key rates at long distance to beat the rate distance limit. Here, applying the sending or not sending TF QKD protocol, we experimentally demonstrate a secure key distribution breaking the absolute key rate limit of repeaterless QKD over 509 km, 408 km ultra-low loss optical fibre and 350 km standard optical fibre. Two independent lasers are used as the source with remote frequency locking technique over 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 rates obtained at different distances are more than 5 times higher than the conditional limit of repeaterless QKD, a bound value assuming the same detection loss in the comparison. The achieved secure key rate is also higher than that a traditional QKD protocol running with a perfect repeaterless QKD device and even if an infinite number of sent pulses. Our result shows that the protocol and technologies applied in this experiment enable TF QKD to achieve high secure key rate at long distribution distance, and hence practically useful for field implementation of intercity QKD.Introduction.-Channel loss seems to be the most severe limitation on the practical application of long distance quantum key distribution (QKD) [1-3], given that quantum signals cannot be amplified. Much efforts have been made towards the goal of a longerdistance for QKD [4][5][6]. Theoretically, the decoy-state method [7][8][9] can improve the key rate of coherent-state based QKD from scaling quadratically to a linear with the channel transmittance, as what behaves of a perfect single-photon source. This method can beat the photonnumber-splitting attack to the imperfect single-photon source and the coherent state is used as if only those single-photon pulses were used for key distillation, and hence it can reach the key rate to a level comparable with that of a perfect single-photon source.

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 demanding is rather tough because it requests 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 lasers' wavelengths and utilize additional phase reference light to estimate and compensate the fiber fluctuation. Further with a single photon detector with high detection rate, we demonstrate twin field quantum key distribution through the sending-or-not-sending protocol with realistic phase drift over 300 km optical fiber spools. We calculate the secure key rates with finite size effect. The secure key rate at 300 km (1.96 × 10 −6 ) is higher than that of the repeaterless secret key capacity (8.64 × 10 −7 ).Introduction.-Although quantum key distribution (QKD) can in principle offer secure private communication [1][2][3][4][5][6][7], there are still some technical limitations on practical long distance quantum communication. Perhaps the most severe of these is channel loss, given that quantum signals cannot be amplified. Much efforts have been made towards QKD over longer-distance. Theoretically, the decoy-state method [8][9][10] can improve the key rate of coherent-state based QKD from scaling quadratically to linearly with the channel transmittance, as what behaves of a perfect single-photon source. This method can defeat the photon-number-splitting attack to the imperfect source and the coherent state is used as if only the single-photon pulses were used for key distillation, and hence it can reach a key rate in the linear scale of channel loss, as the perfect single-photon source does. Remarkable theoretical progress was made toward achieving practical, secure QKD over longer distance with the proposal of twin-field QKD [11], which improves the key rate scaling to follow the square root of the channel transmittance. It shows that, the coherent-state source can actually be an advantage over the single-photon source because the post-selection of phase coherence of the twin fields from Alice and Bob can potentially lead to secure QKD with the encoding state of single-photon and vacuum, and their linear super-positions.This method has the potential to achieve a key rate that scales with the square root of channel transmittance, and can by far break the known distance limit of existing protocols in practical QKD [12][13][14][15][16][17][18][19][20]. The theoretical secure key rate can be even higher than the repeaterless secret key capacities, known as the Takeoka-Guha-Wilde (TGW) bound [19] and the Pirandola-Laurenza-Ottaviani-Bianchi (PLOB) bound [20]. However, considerable work still remains to make this a reality.First, there is the theoretical challenge ...

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