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.

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...

Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available singlephoton detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photonstarved situations. Recent security proofs indicate high-dimensional encoding in the photon arrival times is robust and can be implemented to yield high secure throughput. In this work we demonstrate entanglement-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because of four principal factors: Franson interferometry that does not degrade with loss; error correction coding that can tolerate high error rates; optimized time-energy entanglement generation; and highly efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s −1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.

Increasing the dimensionality of quantum entanglement is a key enabler for high-capacity quantum communications and key distribution [1, 2], quantum computation [3] and information processing [4, 5], imaging [6], and enhanced quantum phase measurement [7,8]. A large Hilbert space can be achieved through entanglement in more than one degree of freedom (known as hyperentanglement [2,7,9]), where each degree of freedom can also be expanded to more than two dimensions (known as high-dimensional entanglement). The high-dimensional entanglement can be prepared in several physical attributes, for example, in orbital angular momentum [1,[10][11][12] and other spatial modes [13][14][15]. The drawback of these high-dimensional spatial states is complicated beam-shaping for entanglement generation and detection, which reduces the brightness of the sources as the dimension scales up, and complicates their use in optical-fiber-based communications systems. In contrast, the continuous-variable energy-time entanglement [16][17][18][19][20][21][22] is intrinsically suitable for high-dimensional coding and, if successful, can potentially be generated and be communicated in the telecommunication network. However, most studies focus on time-bin entanglement, which is discrete-variable entanglement with typical dimensionality of two [23][24][25]. Difficulties in pump-pulse shaping and phase control limit the dimensionality of the time-bin entanglement [26], and high-dimensional time-bin entanglement has not been fully characterized because of the overwhelmingly complicated analyzing interferometers. On the other hand, a biphoton state with a comb-like spectrum could potentially serve for high-dimensional entanglement generation and take full advantage of the continuous-variable energy-time subspace. Based on this state, promising applications have been proposed for quantum computing, secure wavelength-division multiplexing, and dense quantum key distribution [3,27,28]. A phase-coherent biphoton frequency comb (BFC) is also known for 3 its mode-locked behavior in its second-order correlation. Unlike classical frequency combs, where mode-locking directly relies on phase coherence over individual comb lines, the mode-locked behavior of a BFC is the representation of the phase coherence of a biphoton wavepacket over comb-line pairs, and results in periodic recurrent correlation at different time-bins [29, 30]. This time correlation feature can be characterized through quantum interference when passing the BFC through an unbalanced Hong-Ou-Mandel (HOM)-type interferometer [31]. A surprising revival of the correlation dips can be observed at time-bins with half the period of the BFC revival time.However, because of the limited type-I collinear spontaneous parametric downconversion (SPDC) configuration in the prior studies [29], post-selection was necessary for the BFC generation where the signal and idler photons are indistinguishable, limiting the maximum two-photon interference to 50 %.Here we achieve high-dimensional hyperentangle...