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For more than 80 years, the counterintuitive predictions of quantum theoryhave stimulated debate about the nature of reality. In his seminal work, JohnBell proved that no theory of nature that obeys locality and realism canreproduce all the predictions of quantum theory. Bell showed that in any localrealist theory the correlations between distant measurements satisfy aninequality and, moreover, that this inequality can be violated according toquantum theory. This provided a recipe for experimental tests of thefundamental principles underlying the laws of nature. In the past decades,numerous ingenious Bell inequality tests have been reported. However, becauseof experimental limitations, all experiments to date required additionalassumptions to obtain a contradiction with local realism, resulting inloopholes. Here we report on a Bell experiment that is free of any suchadditional assumption and thus directly tests the principles underlying Bell'sinequality. We employ an event-ready scheme that enables the generation ofhigh-fidelity entanglement between distant electron spins. Efficient spinreadout avoids the fair sampling assumption (detection loophole), while the useof fast random basis selection and readout combined with a spatial separationof 1.3 km ensure the required locality conditions. We perform 245 trialstesting the CHSH-Bell inequality $S \leq 2$ and find $S = 2.42 \pm 0.20$. Anull hypothesis test yields a probability of $p = 0.039$ that a local-realistmodel for space-like separated sites produces data with a violation at least aslarge as observed, even when allowing for memory in the devices. This resultrules out large classes of local realist theories, and paves the way forimplementing device-independent quantum-secure communication and randomnesscertification.

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km