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 S = 22.Further improvement is possible by optimizing the entangled-photon sources.
Bell＇s theorem argues the existence of quantum nonlocality which goes basically against the hidden variable theory （HVT）. Many experiments have been done via testing the violations of Bell＇s inequalities to statistically verify the Bell＇s theorem. Alternatively, by testing the Hardy＇s ladder proofs we experimentally demonstrate the deterministic violation of HVT and thus confirm the quantum nonlocality. Our tests are implemented with non-maximal entangled photon pairs generated by spontaneous parametric down conversions （SPDCs）. We show that the degree freedom of photon entanglement could be significantly enhanced by using interference filters. As a consequence, the Hardy＇s ladder proofs could be tested and Bell＇s theorem is verified robustly. The probability of violating the locality reach to 41.9%, which is close to the expectably ideal value 46.4% for the photon pairs with degree of entanglement e = 0.93. The higher violating probability is possible by further optimizing the experimental parameters.
