Paper detail

Heralded amplification of nonlocality via entanglement swapping for long-distance device-independent quantum key distribution

To realize the practical implementation of device-independent quantum key distribution~(DIQKD), the main difficulty is that its security relies on the detection-loophole-free violation of the Clauser-Horne-Shimony-Holt~(CHSH) inequality, i.e. the CHSH value $S>2$, which is easily destroyed by the loss in transmission channels. One of the simplest methods to circumvent it is to utilize the entanglement swapping relay~(ESR). Here, we propose and experimentally test an improved version of the heralded nonlocality amplifier protocol based on the ESR, and numerically show that our scheme is much more robust against the transmission loss than the previously developed protocol. In the experiment, we observe that the obtained probability distribution is in excellent agreement with those expected by the numerical simulation with experimental parameters which are precisely characterized in a separate measurement. Moreover, we experimentally estimate the nonlocality of the heralded state after the transmission of 10~dB loss just before detection. It is estimated to be $S=2.104>2$, which indicates that our final state possesses strong nonlocality even with various experimental imperfections. Our result clarifies an important benchmark of the ESR protocol, and paves the way towards the long-distance realization of the loophole-free CHSH-violation as well as DIQKD.