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arXiv:1609.02282 · Optica

Testing the Bell inequality on frequency-bin entangled photon pairs using time-resolved detection

Xianxin Guo, Yefeng Mei, Shengwang Du

Published Mar 20, 2017• 38 citations

Abstract

Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as a strong witness for quantum entanglement. In previous Bell test experiments with photonic entanglement based on two-photon coincidence measurement, the photon temporal wave packets are absorbed completely by the detectors. That is, the photon coherence time is much shorter than the detection time window. Here we demonstrate generation of frequency-bin entangled narrowband biphotons, and for the first time, test the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality |S|<= 2 for their nonlocal temporal correlations with time-resolved detection. We obtain a maximum |S| value of 2.52+/-0.48 that violates the CHSH inequality. Our result will have applications in quantum information processing involving time-frequency entanglement.

DOI: 10.1364/optica.4.000388

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Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of

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We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between two measurement settings, with each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the four total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test the robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes.

Bell's theorem revealed the fundamental incompatibility between the predictions of quantum mechanics and local realism. Bell inequality violations have since demonstrated quantum nonlocality using photons and internal states of massive particles, but never using their motional states. Here we report the first Bell inequality violation in the motional states of massive particles. Using momentum-entangled pairs of metastable helium atoms manipulated by matter-wave interferometry, we measure a Clauser-Horne-Shimony-Holt (CHSH) Bell parameter of

S = 2.52 \pm 0.17

, violating the CHSH-Bell inequality (

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). Our work completes a long-standing objective in quantum atom optics by extending Bell tests from internal quantum variables to the external degrees of freedom of massive particles, opening a new regime for exploring quantum nonlocality in matter waves and for investigating the interplay between quantum mechanics and gravity.

Bell’s theorem states that quantum mechanics cannot be accounted for by any local theory. One of the examples is the existence of quantum non-locality is essentially violated by the local Bell’s inequality. Therefore, the violation of Bell’s inequality (BI) has been regarded as one of the robust evidences of quantum mechanics. Until now, BI has been tested by many experiments, but the maximal violation (i.e., Cirel’son limit) has never been achieved. By improving the design of entangled sources and optimizing the measurement settings, in this work we report the stronger violations of the Clauser–Horne–Shimony–Holt (CHSH)-type Bell’s inequality. The biggest value of Bell’s function in our experiment reaches to a significant one: S = 2.772± 0.063, approaching to the so-called Cirel’son limit in which the Bell function value is . Further improvement is possible by optimizing the entangled-photon sources.