  Device-independent quantum key distribution (DIQKD) exploits the violation of
a Bell inequality to extract secure key even if the users' devices are
untrusted. Currently, all DIQKD protocols suffer from the secret key capacity
bound, i.e., the secret key rate scales linearly with the transmittance of two
users. Here we propose a heralded DIQKD scheme based on entangled coherent
states to improve entangling rates whereby long-distance entanglement is
created by single-photon-type interference. The secret key rate of our scheme
can significantly outperform the traditional two-photon-type Bell-state
measurement scheme and, importantly, surpass the above capacity bound. Our
protocol therefore is an important step towards a realization of DIQKD and can
be a promising candidate scheme for entanglement swapping in future quantum
internet.
