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.

Introductory paragraphSingle-photon detectors (SPDs) 1 at near-infrared wavelengths with high system detection efficiency (> 90%), low dark count rate (< 1 counts per second, cps), low timing jitter (< 100 ps), and short reset time (< 100 ns) would enable landmark experiments in a variety of fields [2][3][4][5][6] . Although some of the existing approaches to single-photon detection fulfill one or two of the above specifications 1 , to date no detector has met all of the specifications simultaneously. Here we report on a fiber-coupled singlephoton-detection system employing superconducting nanowire single-photon detectors (SNSPDs) 7 that closely approaches the ideal performance of SPDs. Our detector system has a system detection efficiency (SDE), including optical-coupling losses, greater than 90% in the wavelength range λ = 1520 -1610 nm; device dark count rate (measured with the device shielded from room-temperature blackbody radiation) of ≈ 0.01 cps; timing jitter of ≈ 150 ps FWHM; and reset time of 40 ns.

Optical-to-electrical conversion, which is the basis of the operation of optical detectors, can be linear or nonlinear. When high sensitivities are needed, single-photon detectors are used, which operate in a strongly nonlinear mode, their response being independent of the number of detected photons. However, photon-number-resolving detectors are needed, particularly in quantum optics, where n-photon states are routinely produced. In quantum communication and quantum information processing, the photon-numberresolving functionality is key to many protocols, such as the implementation of quantum repeaters 1 and linear-optics quantum computing 2 . A linear detector with single-photon sensitivity can also be used for measuring a temporal waveform at extremely low light levels, such as in longdistance optical communications, fluorescence spectroscopy and optical time-domain reflectometry. We demonstrate here a photon-number-resolving detector based on parallel superconducting nanowires and capable of counting up to four photons at telecommunication wavelengths, with an ultralow dark count rate and high counting frequency.Among the approaches proposed so far for photon-numberresolving (PNR) detection (Table 1) are detectors based on charge integration or field-effect transistors 3-5 , which are, however, affected by long integration times, leading to bandwidths of ,1 MHz. Transition edge sensors 6 operate at 100 mK and show long response times (several microseconds). Approaches based on photomultipliers 7 and avalanche photodiodes, such as the visiblelight photon counter 8,9 , two-dimensional arrays of avalanche photodiodes 10,11 and time-multiplexed detectors 12,13 are not sensitive or are plagued by high dark count rates (DKs) and long dead times in the telecommunication spectral windows. Arrays of single-photon detectors (SPDs) also involve complex readout schemes 11 or separate contacts, amplification and discrimination 14. The parallel nanowire detector (PND) presented here significantly outperforms these approaches in terms of simplicity, sensitivity, speed and multiplication noise.The basic structure of the PND comprises the parallel connection of N superconducting nanowires, each connected in series to a resistor R 0 (Fig.

Photonic-integrated circuits have emerged as a scalable platform for complex quantum systems. A central goal is to integrate single-photon detectors to reduce optical losses, latency and wiring complexity associated with off-chip detectors. Superconducting nanowire single-photon detectors (SNSPDs) are particularly attractive because of high detection efficiency, sub-50-ps jitter and nanosecond-scale reset time. However, while single detectors have been incorporated into individual waveguides, the system detection efficiency of multiple SNSPDs in one photonic circuit—required for scalable quantum photonic circuits—has been limited to <0.2%. Here we introduce a micrometer-scale flip-chip process that enables scalable integration of SNSPDs on a range of photonic circuits. Ten low-jitter detectors are integrated on one circuit with 100% device yield. With an average system detection efficiency beyond 10%, and estimated on-chip detection efficiency of 14–52% for four detectors operated simultaneously, we demonstrate, to the best of our knowledge, the first on-chip photon correlation measurements of non-classical light.

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...

Optical quantum memories are essential elements in quantum networks for long-distance distribution of quantum entanglement. Scalable development of quantum network nodes requires on-chip qubit storage functionality with control of the readout time. We demonstrate a high-fidelity nanophotonic quantum memory based on a mesoscopic neodymium ensemble coupled to a photonic crystal cavity. The nanocavity enables >95% spin polarization for efficient initialization of the atomic frequency comb memory and time bin–selective readout through an enhanced optical Stark shift of the comb frequencies. Our solid-state memory is integrable with other chip-scale photon source and detector devices for multiplexed quantum and classical information processing at the network nodes.

In optics, the ability to measure individual quanta of light (photons) enables a great many applications, ranging from dynamic imaging within living organisms 1 to secure quantum communication 2 . Pioneering photon counting experiments, such as the intensity interferometry performed by Hanbury Brown and Twiss 3 to measure the angular width of visible stars, have played a critical role in our understanding of the full quantum nature of light 4 . As with matter at the atomic scale, the laws of quantum mechanics also govern the properties of macroscopic mechanical objects, providing fundamental quantum limits to the sensitivity of mechanical sensors and transducers. Current research in cavity optomechanics seeks to use light to explore the quantum properties of mechanical systems ranging in size from kilogram-mass mirrors to nanoscale membranes 5 , as well as to develop technologies for precision sensing 6 and quantum information processing 7,8 . Here we use an optical probe and single-photon detection to study the acoustic emission and absorption processes in a silicon nanomechanical resonator, and perform a measurement similar to that used by Hanbury Brown and Twiss to measure correlations in the emitted phonons as the resonator undergoes a parametric instability formally equivalent to that of a laser 9 . Owing to the cavityenhanced coupling of light with mechanical motion, this effective phonon counting technique has a noise equivalent phonon sensitivity of 0.89 6 0.05. With straightforward improvements to this method, a variety of quantum state engineering tasks using mesoscopic mechanical resonators would be enabled 10 , including the generation and heralding of single-phonon Fock states 11 and the quantum entanglement of remote mechanical elements 12,13 . Measurement of the properties of mechanical systems in the quantum regime typically involves heterodyne detection of a coupled optical or electrical field, yielding a continuous signal proportional to the displacement amplitude 14 . An alternative method, particularly suited to optical read-out, is to utilize photon counting as a means to probe the quantum dynamics of the coupled optomechanical system 15,16 . Photon counting can be readily adapted to study intensity correlations in an optical field, and has been used not only in the astronomical studies of thermal light using the technique of Hanbury Brown and Twiss (HBT), but also in early studies of the photon statistics of laser light and single-atom fluorescence 4,17 . In the field of photon-correlation spectroscopy, such intensity interferometry techniques have found widespread application in the measurement of particle and molecular motion in materials 18 . More recently, photon counting of Raman scattering events in diamond has heralded and verified the quantum entanglement of a terahertz phonon shared between two separate bulk diamond crystals 13 . In the case of engineered cavity optomechanical systems, much longer phonon coherence times are attainable, albeit at lower mechanical frequencies (megahe...

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.