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Quantum key distribution is a way to distribute secret keys to distant userswith information theoretic security and key rates suitable for real-worldapplications. Its rate-distance figure, however, is limited by the natural lossof the communication channel and can never surpass a theoretical limit known aspoint-to-point secret key capacity. Recently, a new type of quantum keydistribution with an intermediate relay was proposed to overcome this limit (M.Lucamarini, Z. L. Yuan, J. F. Dynes and A. J. Shields, Nature, 2018). However,a standard application of the decoy state method limited the security analysisof this scheme to hold under restrictive assumptions for the eavesdropper.Hence, overcoming the point-to-point secret key capacity with aninformation-theoretic secure scheme is still an open question. Here, we proposea novel way to use decoy states to answer this question. The key idea is toswitch between a Test mode and a Code mode, the former enabling the decoy stateparameter estimation and the latter generating a key through a phase encodingprotocol. This way, we confirm the scaling properties of the original schemeand overcome the secret key capacity at long distances. Our work plays a keyrole to unlock the potential of practical secure quantum communications.

Information theoretic security of quantum key distribution overcoming the repeaterless secret key capacity bound