More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.

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.

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.

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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.But if [a hidden variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says. -John Stewart Bell [1] Quantum mechanics at its heart is a statistical theory. It cannot with certainty predict the outcome of all single events, but instead it predicts probabilities of outcomes. This probabilistic nature of quantum theory is at odds with the determinism inherent in Newtonian physics and relativity, where outcomes can be exactly predicted given sufficient knowledge of a system. Einstein and others felt that quantum mechanics was incomplete. Perhaps quantum systems are controlled by variables, possibly hidden from us [2], that determine the outcomes of measurements. If we had direct access to these hidden variables, then the outcomes of all measurements performed on quantum systems could be predicted with certainty. De Broglie's 1927 pilot-wave theory was a first attempt at formulating a hidden variable theory of quantum physics [3]; it was completed in 1952 by David Bohm [4,5]. While the pilot-wave theory can reproduce all of the predictions of quantum mechanics, it has the curious feature that hidden variables in one location can instantly change values because of events happening in distant locations. This seemingly violates the locality principle from relativity, which says that objects cannot signal one another faster than the speed of light. In 1935 the nonlocal feature of quantum systems was popularized by Einstein, Podolsky, and Rosen [6], and is something Einstein later referred to as "spooky actions at a distance" [7]. But in 1964 John Bell showed that it is impossible to construct a hidden variable theory that obeys locality and simultaneously reproduces all of the predictions of quantum mechanics [8]. Bell's theorem fundamentally changed our understanding of quantum theory and today stands as a cornerstone of modern quantum information science.Bell's theorem does not prove the validity of quantum mechanics, but it does allow us to test the hypothesis that nature is governed by local realism. The principle of realism says that any syst...

Abstract:We demonstrate a high bit-rate quantum random number generator by interferometric detection of phase diffusion in a gain-switched DFB laser diode. Gain switching at few-GHz frequencies produces a train of bright pulses with nearly equal amplitudes and random phases. An unbalanced Mach-Zehnder interferometer is used to interfere subsequent pulses and thereby generate strong random-amplitude pulses, which are detected and digitized to produce a high-rate random bit string. Using established models of semiconductor laser field dynamics, we predict a regime of high visibility interference and nearly complete vacuum-fluctuation-induced phase diffusion between pulses. These are confirmed by measurement of pulse power statistics at the output of the interferometer. Using a 5.825 GHz excitation rate and 14-bit digitization, we observe 43 Gbps quantum randomness generation.

We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below 10 −5 and strong metrological randomness assurances. This randomness generation strategy satisfies the stringent requirements for unpredictable basis choices in current "loophole-free Bell tests" of local realism [Hensen et al., Nature (London) 526, 682 (2015); Giustina et al., Phys. Rev. Lett. 115, 250401 (2015); Shalm et al., Phys. Rev. Lett. 115, 250402 (2015)].PACS numbers: 03.65.Ud, 03.65.Ta, 42.50.Ct, Quantum nonlocality [1] is one of the most striking predictions to emerge from quantum theory. Beyond their fundamental interest, loophole-free Bell tests enable powerful "device independent" information protocols, guaranteed by the impossibility of faster-than-light communication [2]. Bell tests and device-independent protocols employ spacelike separation of measurements to guarantee the nonlocality of correlations [3][4][5][6][7][8] and the monogamy of correlations under the no-signaling principle [9][10][11]. To be secure, they must close two spacetime loopholes: no basis choice may influence a distant particle (locality loophole), and the entanglement generation must not influence the basis choices (freedom-ofchoice loophole). Current efforts [6,7,[12][13][14] to simultaneously close the detection [4,6,7], locality [3], and freedom-of-choice (FoC) [5,8] loopholes require random number generators (RNGs) with an unprecedented combination of speed, unpredictability, and confidence [15][16][17].Here we combine ultrafast RNG by accelerated laser phase diffusion [18][19][20] with real-time randomness extraction and metrological randomness assurances [21] to produce a RNGs suitable for loophole-free Bell tests. Because the laser phase diffusion is driven by effects, including spontaneous emission, that are unpredictable both in quantum theory and in an important class of stochastic hidden variable theories, the source can be used to address the "freedom-of-choice" loophole [22]. Using a detailed and validated model of the signal generation process, we show the effectiveness of parity-bit randomness extraction of this source. Under paranoid assumptions, we infer excess predictability below 10 −5 at 6σ statistical confidence for output based on phase-diffusion events less than 36 ns old. A statistical analysis based on 2.3 Tbits of random data supports the metrological assessment of extreme unpredictability. The results enable definitive nonlocality experiments and secure communications without the need for trusted devices [9,11,23,24].As shown in Fig. 1, the locality and freedom-of-choice loopholes can be closed by spacelike separation of the random events that determine the basis choice from the distant detection and from the production of the pairs of particles, respectively [10]. This requires generation of randomness in a time window shorter than the light time between the detectors. Closing the "detection loophole" requires high efficiency and motivates p...

Random number generators are essential to ensure performance in information technologies, including cryptography, stochastic simulations and massive data processing. The quality of random numbers ultimately determines the security and privacy that can be achieved, while the speed at which they can be generated poses limits to the utilisation of the available resources. In this work we propose and demonstrate a quantum entropy source for random number generation on an indium phosphide photonic integrated circuit made possible by a new design using two-laser interference and heterodyne detection. The resulting device offers high-speed operation with unprecedented security guarantees and reduced form factor. It is also compatible with complementary metal-oxide semiconductor technology, opening the path to its integration in computation and communication electronic cards, which is particularly relevant for the intensive migration of information processing and storage tasks from local premises to cloud data centres.http://dx