  Quantum key distribution is a way to distribute secret keys to distant users
with information theoretic security and key rates suitable for real-world
applications. Its rate-distance figure, however, is limited by the natural loss
of the communication channel and can never surpass a theoretical limit known as
point-to-point secret key capacity. Recently, a new type of quantum key
distribution 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 analysis
of this scheme to hold under restrictive assumptions for the eavesdropper.
Hence, overcoming the point-to-point secret key capacity with an
information-theoretic secure scheme is still an open question. Here, we propose
a novel way to use decoy states to answer this question. The key idea is to
switch between a Test mode and a Code mode, the former enabling the decoy state
parameter estimation and the latter generating a key through a phase encoding
protocol. This way, we confirm the scaling properties of the original scheme
and overcome the secret key capacity at long distances. Our work plays a key
role to unlock the potential of practical secure quantum communications.
