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

For more than 80 years, the counterintuitive predictions of quantum theory have stimulated de-bate about the nature of reality 1 . In his seminal work 2 , John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, numerous ingenious Bell inequality tests have been reported 3-12 . However, because of experimental limitations, all experiments to date required additional assumptions to obtain a contra-diction with local realism, resulting in loopholes 12-15 . Here we report on a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell’s inequality. We employ an event-ready scheme 2,16,17 that enables the generation of high-fidelity entanglement between distant electron spins. Efficient spin readout avoids the fair sampling assumption (detec-tion loophole 13,14 ), while the use of fast random basis selection and readout combined with a spatial separation of 1.3 km ensure the required locality conditions 12 . We perform 245 trials testing the CHSH-Bell inequality 18 S ≤ 2 and find S = 2 . 42 ± 0 . 20. A null hypothesis test yields a probability of p = 0 . 039 that a local-realist model for space-like separated sites produces data with a violation at least as large as observed, even when allowing for memory 15,19 in the devices. This result rules out large classes of local realist theories, and paves the way for implementing device-independent quantum-secure communication 20 and randomness certification 21,22 .