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Quantum key distribution (QKD)1,2 offers a long-term solution to secure key exchange. Due to photon loss in transmission, it was believed that the repeaterless key rate is bounded by a linear function of the transmittance, O(η) (refs. 3,4), limiting the maximal secure transmission distance5,6. Recently, a novel type of QKD scheme has been shown to beat the linear bound and achieve a key rate performance of $$O(\sqrt{\eta })$$ (refs. 7–9). Here, by employing the laser injection technique and the phase post-compensation method, we match the modes of two independent lasers and overcome the phase fluctuation. As a result, the key rate surpasses the linear bound via 302 km and 402 km commercial-fibre channels, over four orders of magnitude higher than existing results5. Furthermore, our system yields a secret key rate of 0.118 bps with a 502 km ultralow-loss fibre. This new type of QKD pushes forward long-distance quantum communication for the future quantum internet. Phase-matching quantum key distribution is implemented with a 502 km ultralow-loss optical fibre. The fluctuations of the laser initial phases and frequencies are suppressed by the laser injection technique and the phase post-compensation method.

Quantum key distribution (QKD) can provide information theoretically secure key exchange even in the era of quantum computer. However, QKD requires the classical channel to be authenticated, and the current method is pre-sharing symmetric keys. For a QKD network of $n$ users, this method requires $C_n^2 = n(n-1)/2$ pairs of symmetric keys to realize pairwise interconnection. In contrast, with the help of mature public key infrastructure (PKI) and post-quantum cryptography (PQC) with quantum resistant security, each user only needs to apply for a digital certificate from certificate authority (CA) to achieve efficient and secure authentication for QKD. We only need to assume the short-term security of the PQC algorithm to achieve the long-term security of the distributed keys. Here, we experimentally verified the feasibility, efficiency and stability of the PQC algorithm in QKD authentication, and demonstrated the advantages when new users join the QKD network. Using PQC authentication we only need to believe the CA is safe, rather than all trusted relays. QKD combined with PQC authentication will greatly promote and extend the application prospects of quantum safe communication., Comment: 8 pages, 6 figures

Depletion effects are well known to lead to phase separation in microsystems consisting of large and small particles with short-range repulsive interactions that act over macromolecular length scales. The equilibrium mechanics between an enveloped colloidal particle and a biomembrane caused by entropy is investigated by using a continuum model. We show that the favorable contact energy stems from entropy, which is sufficient to drive engulfment of the colloidal particle, and deformation of the biomembrane determines the resistance to the engulfment of the colloidal particle. The engulfment process depends on the ratio of the radii of the larger particle and smaller particles and the bending rigidity. The results show insights into the effects of depletion on biomembrane budding and nanoparticle transportation by a vesicle.

Based on the model of the strong correlation of counterions condensed on DNA molecule, by tailoring interaction potential, interduplex spacing and correlation spacing between condensed counterions on DNA molecule and interduplex spacing fluctuation strength, toroidal configuration, rod-like configuration and two-hole configurations are possible. The size effects of counterion structure on the toroidal structure can be detected by this model. The autocorrelation function of the tangent vectors is found as an effective way to detect the structure of toroidal conformations and the generic pathway of the process of DNA condensation. The generic pathway of all of the configurations involves an initial nucleation loop, and the next part of the DNA chain is folded on the top of the initial nucleation loop with different manners, in agreement with the recent experimental results.