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.

A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or "trajectory" that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.

We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first reported experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate "device-independent" private quantum random numbers at rates over 4 orders of magnitude beyond previous experiments.This document has been published at http://prl.aps.org/abstract/PRL/v111/i13/e130406 in Phys. Rev. Lett.PACS numbers: 03.65. Ud, 03.67.Ac, 42.50.Xa, 03.67.Bg In 1935, Einstein, Podolsky, and Rosen suggested that certain quantum mechanical states must violate one or both of the fundamental classical assumptions of locality (sufficiently distant events cannot change the outcome of a nearby measurement) and realism (the outcome probabilities of potential measurements depend only on the state of the system). These nonclassical two-particle states exhibit multiple-basis correlations (or anti-correlations), and are referred to as "entangled". Because locality and realism are so fundamental to classical intuition, a central debate in 20th century physics [1] revolved around the following question: could an alternative to quantum mechanics-a local realistic theory-explain entanglements seemingly nonclassical correlations? In 1964, John Bell devised a way to in principle answer this question experimentally, by analyzing the limit of allowed correlations between measurements made on an ensemble of any classical system [2]. If performed under sufficiently ideal conditions, a violation of Bells inequality would conclusively rule out all possible local realistic theories. Although entanglement has been experimentally demonstrated and the Bell inequality violated in a myriad of non-ideal experiments [3][4][5][6][7][8][9][10][11][12], each of these experiments fails to overcome at least one of two critical obstacles.The first obstacle-the "locality loophole"-addresses the possibility that a local realistic theory might rely on some type of signal sent from one entangled particle to its partner (e.g., a signal containing information about the specific measurement carried out on the first particle), or from the measurement apparatus to the source (known as the freedom of choice loophole). These loopholes have thus far only been closed using entangled photons [8, 13]; photons traveling in different directions can be measured at places and times which are relativistically strictly simultaneous (i.e., in a space-like separated configuration). The second obstacle-the "detection loophole"-addresses the fact that even maximally entangled particles, when measured with low-quantum-efficiency detectors, will produce experimental results that can be explained by a local realistic theory. To avoid this, almos...