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.

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Abstract:The violation of a Bell inequality is an experimental observation that forces one to abandon a local realistic worldview, namely, one in which physical properties are (probabilistically) defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. All such experimental violations require additional assumptions depending on their specific construction making them vulnerable to so-called "loopholes." Here, we use photons and high-efficiency superconducting detectors to violate a Bell inequality closing the fair-sampling loophole, i.e. without assuming that the sample of measured photons accurately represents the entire ensemble. Additionally, we demonstrate that our setup can realize one-sided device-independent quantum key distribution on both sides. This represents a significant advance relevant to both fundamental tests and promising quantum applications. Introduction:In 1935, Einstein, Podolsky, and Rosen (EPR) (1) argued that quantum mechanics is incomplete when assuming that no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality. They considered measurements on spatially separated pairs of entangled particles. Measurement on one particle of an entangled pair projects the other instantly on a well-defined state, independent of their spatial separation. In 1964, Bell (2) showed that no local realistic theory can reproduce all quantum mechanical predictions for entangled states. His renowned Bell inequality proved that there is an upper limit to the strength of the observed correlations predicted by local realistic theories. Quantum theory's predictions violate this limit.