Heralded amplification of nonlocality via entanglement swapping

To observe the loophole-free violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality between distant two parties, i.e. the CHSH value $S>2$, the main limitation of distance stems from the loss in the transmission channel. The entanglement swapping relay (ESR) is a simple way to amplify the signal and enables us to evade the impact of the transmission loss. Here, we experimentally test the heralded nonlocality amplifier protocol based on the ESR. 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 final detection. The estimated CHSH value is $S=2.113>2$, which indicates that our final state possesses nonlocality even with transmission loss and 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 device-independent quantum key distribution. (paper)