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.

Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and various materials properties [1][2][3].Without quantum enhancement, the precision limit in determining an unknown optical phase ϕ-i.e. the minimum uncertainty ∆ϕ-is the shot noise limit (SNL): ∆ϕ SN L = 1/ √ n, where n is the number of resources (e.g. photons) used. Entangled photons promise measurement sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is a path-entangled state of definite number of photons N . Despite theoretical proposals stretching back decades [3,4], no measurement using such photonic (definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all demonstrations have employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use an ultra-high efficiency source and high efficiency superconducting photon detectors to respectively make and measure a two-photon instance of the maximally-phase-sensitive NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit-that is, without artificially correcting for loss or any other source of imperfection. Our results enable quantum-enahanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.It has been known for several decades that probing with various optical quantum states can achieve phase super-sensitivity, i.e measurement of the phase with an uncertainty below the SNL [3,4]. It has been shown theoretically that multi-photon entangled states, such as NOON states, may achieve super-sensitivity and can, in principle, saturate the Heisenberg limit (HL), the ultimate bound on sensitivity [3,4,7]. For this reason, they are of great interest for maximising the information that can be collected per photon, which is useful for investigating sensitive samples [8]. NOON states are superpositions of N photons across two arms of an interferometer, each of which is a single optical mode:We use the term photonic to refer to states like this, because they possess definite photon number, and these photons are counted in detection. By contrast, we exclude from term "photonic" schemes using states of indefinite photon number and continuous wave-like measurement, such as squeezed states and homodyne detection. Such techniques have genuinely beaten the SNL, e.g. refs [5,6], but work over narrow bandwidths and cannot directly achieve the theoretical maximal sensitivity per resource. Super-resolution, however, is not enough by itself to surpass the SNL [9,20]: a high interference fringe visibility, and high transmission and detection efficiency are also required-they must exceed the t...

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.