Abstract
To observe the loophole-free violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality between distant two parties, i.e. the CHSH value , 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 , 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.
Highlights
Nonlocality is one of the most interesting features of quantum mechanics which can be tested by the celebrated Bell inequality [1, 2]
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 destroyed by the loss in transmission channels
We show the following major progress in this direction: we propose an improved scheme of a heralded nonlocality amplifier based on the entanglement swapping relay (ESR), perform it experimentally, and estimate the nonlocality of the experimentally generated state by the ESR-based heralding, which shows the violation of the CHSH inequality even after transmitting through a channel with loss corresponding to the 50 km-optical fiber
Summary
Nonlocality is one of the most interesting features of quantum mechanics which can be tested by the celebrated Bell inequality [1, 2]. The detection efficiencies of our system are not in the range of directly observing the violation of the CHSH inequality of the heralded state, the probability distributions obtained by the experiment are in excellent agreement with those independently obtained by our numerical model that includes imperfections This feature allows us to estimate the nonlocality and the density matrix of the experimentally heralded state before the final detection. The estimated CHSH value is S = 2.104, which shows that the experimentally heralded state has significant nonlocality, while the fidelity of the heralded state to the two-qubit maximally entangled state is estimated to be 0.47 This result indicates that we successfully amplified the nonlocality of the SPDC-based entangled photons, which are degraded by losses in the transmission channels, via the ESR.
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