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Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality 1 – 3 can be experimentally demonstrated in Bell tests 4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes 5 succeeded. Such experiments have been performed with spins in nitrogen–vacancy centres 6 , optical photons 7 – 9 and neutral atoms 10 . Here we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology 11 . To evaluate a Clauser–Horne–Shimony–Holt-type Bell inequality 4 , we deterministically entangle a pair of qubits 12 and perform fast and high-fidelity measurements 13 along randomly chosen bases on the qubits connected through a cryogenic link 14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell’s inequality with a P value smaller than 10 −108 . Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics 15 . A loophole-free violation of Bell’s inequality with superconducting circuits shows that non-locality is a viable new resource in quantum information technology realized with superconducting circuits, promising many potential applications.

Bell-type inequalities are proven using oversimplified probabilistic models and/or counterfactual definiteness (CFD). If setting-dependent variables describing measuring instruments are correctly introduced, none of these inequalities may be proven. In spite of this, a belief in a mysterious quantum nonlocality is not fading. Computer simulations of Bell tests allow people to study the different ways in which the experimental data might have been created. They also allow for the generation of various counterfactual experiments’ outcomes, such as repeated or simultaneous measurements performed in different settings on the same “photon-pair”, and so forth. They allow for the reinforcing or relaxing of CFD compliance and/or for studying the impact of various “photon identification procedures”, mimicking those used in real experiments. Data samples consistent with quantum predictions may be generated by using a specific setting-dependent identification procedure. It reflects the active role of instruments during the measurement process. Each of the setting-dependent data samples are consistent with specific setting-dependent probabilistic models which may not be deduced using non-contextual local realistic or stochastic hidden variables. In this paper, we will be discussing the results of these simulations. Since the data samples are generated in a locally causal way, these simulations provide additional strong arguments for closing the door on quantum nonlocality.

A Bell test is a randomized trial that compares experimental observations against the philosophical worldview of local realism 1 , in which the properties of the physical world are independent of our observation of them and no signal travels faster than light. A Bell test requires spatially distributed entanglement, fast and high-efficiency detection and unpredictable measurement settings 2 , 3 . Although technology can satisfy the first two of these requirements 4 – 7 , the use of physical devices to choose settings in a Bell test involves making assumptions about the physics that one aims to test. Bell himself noted this weakness in using physical setting choices and argued that human ‘free will’ could be used rigorously to ensure unpredictability in Bell tests 8 . Here we report a set of local-realism tests using human choices, which avoids assumptions about predictability in physics. We recruited about 100,000 human participants to play an online video game that incentivizes fast, sustained input of unpredictable selections and illustrates Bell-test methodology 9 . The participants generated 97,347,490 binary choices, which were directed via a scalable web platform to 12 laboratories on five continents, where 13 experiments tested local realism using photons 5 , 6 , single atoms 7 , atomic ensembles 10 and superconducting devices 11 . Over a 12-hour period on 30 November 2016, participants worldwide provided a sustained data flow of over 1,000 bits per second to the experiments, which used different human-generated data to choose each measurement setting. The observed correlations strongly contradict local realism and other realistic positions in bipartite and tripartite 12 scenarios. Project outcomes include closing the ‘freedom-of-choice loophole’ (the possibility that the setting choices are influenced by ‘hidden variables’ to correlate with the particle properties 13 ), the utilization of video-game methods 14 for rapid collection of human-generated randomness, and the use of networking techniques for global participation in experimental science. The BIG Bell Test, which used an online video game with 100,000 participants worldwide to provide random bits to 13 quantum physics experiments, contradicts the Einstein–Podolsky–Rosen worldview of local realism.