Loophole-free test of local realism via Hardy's violation

Bell's theorem states that quantum mechanical description on physical quantity cannot be fully explained by local realistic theories, and lays solid basis for various quantum information applications. Hardy's paradox is celebrated to be the simplest form of Bell's theorem concerning its "All versus Nothing" way to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of experimental systems, which constitute potential loopholes for faithfully testing local realistic theories. Here, we experimentally demonstrate Hardy's nonlocality through a photonic entanglement source. By achieving a detection efficiency of 82.2%, a quantum state fidelity of 99.10% and applying high speed quantum random number generators for measurement setting switching, the experiment is implemented in a loophole-free manner. During 6 hours of running, a strong violation of P_Hardy=4.646× 10^-4 up to 5 standard deviations is observed with 4.32× 10^9 trials. A null hypothesis test shows that the results can be explained by local realistic theories with an upper bound probability of 10^-16348. These testing results present affirmative evidence against local realism, and provide an advancing benchmark for quantum information applications based on Hardy's paradox.