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. theCHSHvalue S > 2, themain limitation of distance stems fromthe 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. Weobserve 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 CHSHvalue 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 longdistance realization of the loophole-free CHSH-violation as well as device-independent quantum key distribution.