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 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 provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.
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 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 provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.
Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as ``the simplest form of Bell's theorem.'' In this work, we advance the study of Hardy's paradox based on Bell's inequality. Our formalism is essentially equivalent to the ``logical Bell inequality'' formalism developed by Abramsky and Hardy, but ours is more easily applied to experimental tests. Remarkably, we find that not only for a two-qubit two-setting case but also for a two-qubit four-setting case, we can construct stronger Hardy-type paradoxes based on Bell's inequality, whose successful probabilities can attain four times and seven times larger than the original one, respectively, thus providing more friendly tests for experiment. Meanwhile, we experimentally test the stronger Hardy-type paradoxes in a two-qubit system. Within the experimental errors, the experimental results coincide with the theoretical predictions.
John Bell’s theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell’s inequalities. Employing modifications of Bell’s inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.
Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect.
"In 1935, Einstein, Podolsky, and Rosen questioned whether quantum mechanics can be complete, as it seemingly does not adhere to a natural view of reality: local realism, which is the notion that an event can only be influenced by events in the past lightcone, and can only influence events in the future lightcone. This question sparked a philosophical debate that lasted for three decades, until John Bell demonstrated that not only are quantum mechanics and local realism philosophically incompatible, but they predict different statistical results for an appropriate set of measurements on entangled particles, which changed the debate to a scientific discussion. Since then, Bell inequality violations have occurred in a plethora of systems, hinting that local realism is indeed wrong. However, every experiment had imperfections that complicated the interpretation --- the experiments had so-called ""loopholes"" which allowed local realism to persist. In this manuscript, we present our work in using optimized sources of entangled photons to perform the long-sought loophole-free Bell test. This landmark experiment invalidates local realism to the best that science will allow. Beyond answering questions on reality, these Bell tests have a important application in generating provably-secure private random numbers, which then can be used as a seed for cryptographic applications. Not only do we demonstrate that nonlocality must exist, but we begin an experimental exploration in an attempt to understand and quantify this nonlocality. We do so by considering all theories that obey no-signaling (or relativistic causality). In our experiments, we observe the counter-intuitive feature of measuring more nonlocality with less entangled states. We also place a bound on the predictive power of any theory that obeys relativistic causality. And finally, we are able to measure quantum correlations only attainable through complex qubits. This work merely begins to probe the quantum boundary, beginning a journey that may someday find evidence of a beyond-quantum theory."
We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first reported experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate "device-independent" private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.
We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p values as small as 5.9×10^{-9} for our Bell violation while maintaining the spacelike separation of our events. We estimate the degree to which a local realistic system could predict our measurement choices. Accounting for this predictability, our smallest adjusted p value is 2.3×10^{-7}. We therefore reject the hypothesis that local realism governs our experiment.