Abstract:The violation of a Bell inequality is an experimental observation that forces one to abandon a local realistic worldview, namely, one in which physical properties are (probabilistically) defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. All such experimental violations require additional assumptions depending on their specific construction making them vulnerable to so-called "loopholes." Here, we use photons and high-efficiency superconducting detectors to violate a Bell inequality closing the fair-sampling loophole, i.e. without assuming that the sample of measured photons accurately represents the entire ensemble. Additionally, we demonstrate that our setup can realize one-sided device-independent quantum key distribution on both sides. This represents a significant advance relevant to both fundamental tests and promising quantum applications. Introduction:In 1935, Einstein, Podolsky, and Rosen (EPR) (1) argued that quantum mechanics is incomplete when assuming that no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality. They considered measurements on spatially separated pairs of entangled particles. Measurement on one particle of an entangled pair projects the other instantly on a well-defined state, independent of their spatial separation. In 1964, Bell (2) showed that no local realistic theory can reproduce all quantum mechanical predictions for entangled states. His renowned Bell inequality proved that there is an upper limit to the strength of the observed correlations predicted by local realistic theories. Quantum theory's predictions violate this limit.

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...

We have created heralded coherent state superpositions (CSS), by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our highefficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This is the first experiment enabled by and utilizing the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean photon number of 2.75 +0.06 −0.24 and a fidelity of 0.59 +0.04 −0.14 with an ideal CSS. This confirms that subtracting more photons results in higher-amplitude CSSs.PACS numbers: 42.50. Dv, 42.50.Xa, 03.65.Ta, 03.65.Wj A coherent state of the electromagnetic field is often considered the most classical-like pure state, but a superposition of two coherent states with opposite phases has interesting quantum features. For example, coherent state superpositions (CSS) can be exploited for performing quantum information tasks and high precision measurements. CSSs are also of fundamental interest: When they contain many photons they are superpositions of macroscopically distinguishable states often called "Schrödinger cat states". Schrödinger's Gedanken experiment of 1935 described a cat apparently held in a superposition of alive and dead states [1], but many researchers now use "Schrödinger cat" to refer to a quantum state that is a superposition of two highly distinguishable classical states such as a CSS of high amplitude or mean number of photons [2]. CSSs have been prepared in traveling optical modes with a mean of up to 2.0 optical photons by heralding [3][4][5][6][7]. With sufficiently high quality and well characterized CSSs, one can in principle quantum compute using simple linear optical components and homodyne measurements [8]. Less ambitiously, they can serve as flying qubits for quantum communication. In addition to potentially simple processing, advantages of CSSs in traveling optical modes include fast linear manipulations, transport over large distances, robustness if loss is controlled, and simple conversion to entangled optical states, all at room temperature.The CSSs that we discuss here are superpositions of two coherent states | ± α of a single mode of light, where +α and −α are the states' complex mode amplitudes. Our experiments aim to prepare two special instances of these CSSs: the odd and even CSSs defined as the superpositions |−α ± |α (unnormalized). These are distinguished by having only even (+) or odd (−) numbers of photons. For |α| 1, the states' mean number of photons, n , is approximately |α| 2 . Two quality measures for experimental CSSs are the fidelity of the created state with the nearest ideal CSS and the magnitude of the amplitude of this ideal CSS. There are two reasons to aim for large amplitude CSSs. The first is that to be useful for superresolution metrology, the probability2 ) with which the superposed coherent states can be distinguished must be close to one. To achieve p 0 > 0.99 requires |α| > 1.52. The second is t...

Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted. A conclusive demonstration of steering through the violation of a steering inequality is of considerable fundamental interest and opens up applications in quantum communication. To date, all experimental tests with single-photon states have relied on post selection, allowing untrusted devices to cheat by hiding unfavourable events in losses. Here we close this 'detection loophole' by combining a highly efficient source of entangled photon pairs with superconducting transition-edge sensors. We achieve an unprecedented ∼62% conditional detection efficiency of entangled photons and violate a steering inequality with the minimal number of measurement settings by 48 s.d.s. Our results provide a clear path to practical applications of steering and to a photonic loophole-free Bell test.

We present a compact packaging technique for coupling light from a single-mode telecommunication fiber to cryogenic single-photon sensitive devices. Our single-photon detectors are superconducting transition-edge sensors (TESs) with a collection area only a factor of a few larger than the area of the fiber core which presents significant challenges to low-loss fiber-to-detector coupling. The coupling method presented here has low loss, cryogenic compatibility, easy and reproducible assembly and low component cost. The system efficiency of the packaged single-photon counting detectors is verified by the "triplet method" of power-source calibration along with the "multiple attenuator" method that produces a calibrated single-photon flux. These calibration techniques, when used in combination with through-wafer imaging and fiber back-reflection measurements, give us confidence that we have achieved coupling losses below 1% for all devices packaged according to the self-alignment method presented in this paper.

Abstract:Single photons are an important prerequisite for a broad spectrum of quantum optical applications. We experimentally demonstrate a heralded single-photon source based on spontaneous parametric down-conversion in collinear bulk optics, and fiber-coupled bolometric transition-edge sensors. Without correcting for background, losses, or detection inefficiencies, we measure an overall heralding efficiency of 83 %. By violating a Bell inequality, we confirm the single-photon character and high-quality entanglement of our heralded single photons which, in combination with the high heralding efficiency, are a necessary ingredient for advanced quantum communication protocols such as one-sided deviceindependent quantum key distribution. *Partial contribution of NIST, an agency of the U.S. government, not subject to copyright Fig. 1. Heralded single-photon source based on correlated photon pairs. Such sources are a prerequisite to a multitude of quantum optical experiments. In an ideal single-photon source, a photon detected in the heralding arm indicates a partner photon in the signal arm.

Abstract:The integrated optical circuit is a promising architecture for the realization of complex quantum optical states and information networks. One element that is required for many of these applications is a highefficiency photon detector capable of photon-number discrimination. We present an integrated photonic system in the telecom band at 1550 nm based on UV-written silica-on-silicon waveguides and modified transition-edge sensors capable of number resolution and over 40 % efficiency. Exploiting the mode transmission failure of these devices, we multiplex three detectors in series to demonstrate a combined 79 % ± 2 % detection efficiency with a single pass, and 88 % ± 3 % at the operating wavelength of an on-chip terminal reflection grating. Furthermore, our optical measurements clearly demonstrate no significant unexplained loss in this system due to scattering or reflections. This waveguide and detector design therefore allows the placement of number-resolving single-photon detectors of predictable efficiency at arbitrary locations within a photonic circuit -a capability that offers great potential for many quantum optical applications. *Contribution of NIST, an agency of the U.S. government, not subject to copyright

Integration is currently the only feasible route toward scalable photonic quantum processing devices that are sufficiently complex to be genuinely useful in computing, metrology, and simulation. Embedded on-chip detection will be critical to such devices. We demonstrate an integrated photon-number-resolving detector, operating in the telecom band at 1550 nm, employing an evanescently coupled design that allows it to be placed at arbitrary locations within a planar circuit. Up to five photons are resolved in the guided optical mode via absorption from the evanescent field into a tungsten transition-edge sensor. The detection efficiency is 7.2 ± 0.5 %. The polarization sensitivity of the detector is also demonstrated. Detailed modeling of device designs shows a clear and feasible route to reaching high detection efficiencies.Photonics provides a promising path for building and using complex quantum systems for both exploring fundamental physics and delivering quantum-enhanced technologies in information processing, metrology, and communications. Currently, the only feasible route toward sufficient complexity is integration, due to the high density of optical modes that can be contained within a single device and the extraordinary level of control that can be exercised over them. Although much research has gone into developing integrated elements at telecom wavelengths for classical applications, their use in the quantum regime has been limited, in large part because of intrinsic inefficiencies in input coupling, detector coupling, and propagation. The effect of these inefficiencies is to reduce or remove any quantum advantage attainable with a given device [1][2][3][4][5][6][7].Current single-photon-sensitive detectors for telecom wavelengths include avalanche photodiodes (APDs) [8], superconducting nanowires [9], and transition-edge sensors (TESs) [10,11]. In x Ga 1-x As APDs, the only commercially available telecom-band, single-photon-sensitive detectors, suffer from high dark-count rates, whereas nanowire detectors have much lower dark-count rates, are extremely fast, and can have high quantum efficiencies comparable to those of In x Ga 1-x As APDs [12]. In order to achieve high efficiencies with these normal incidence detectors, care must be taken to impedance match the incident field to the detector in order to avoid reflections of the optical signal. Moreover, normal incidencedetection schemes are intrinsically limited to monitoring the modes that emerge from the end facet of the device. As a result, inferring information about a quantum state or circuit element inside a device will only become more problematic as circuits move toward the complexities required to study effects beyond the scope of classical computational power [7,13,14]. Developing high-efficiency detectors that are compatible with these complex, high-density systems is therefore a critical enabling step for quantum photonics.In this paper, we demonstrate the operation of a new concept for broadband, efficient, single-photon detection, evanesc...