Loophole-Free Test of Local Realism via Hardy’s Violation

Bell's theorem states that the quantum mechanical description of physical quantities cannot be fully explained by local realistic theories, laying a solid basis for various quantum information applications. Hardy's paradox is celebrated as the simplest form of Bell's theorem concerning its "All versus Nothing" approach to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of the experimental systems, and these assumptions 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 the measurement setting switching, the experiment is implemented in a loophole-free manner. During 6 h of running, a strong violation of P₇₀ₑ₃ₘ=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 provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.