Ultra-fast quantum randomness generation by accelerated phase diffusion in a pulsed laser diode

Quantum random number generation based on phase reconstruction

Quantum random number generator (QRNG) utilizes the intrinsic randomness of quantum systems to generate completely unpredictable and genuine random numbers, finding wide applications across many fields. QRNGs relying on the phase noise of a laser have attracted considerable attention due to their straightforward system architecture and high random number generation rates. However, traditional phase noise QRNGs suffer from a 50% loss of quantum entropy during the randomness extraction process. In this paper, we propose a phase-reconstruction quantum random number generation scheme, in which the phase noise of a laser is reconstructed by simultaneously measuring the orthogonal quadratures of the light field using balanced detectors. This enables direct discretization of uniform phase noise, and the min-entropy can achieve a value of 1. Furthermore, our approach exhibits inherent robustness against the classical phase fluctuations of the unbalanced interferometer, eliminating the need for active compensation. Finally, we conducted experimental validation using commercial optical hybrid and balanced detectors, achieving a random number generation rate of 1.96 Gbps at a sampling rate of 200 MSa/s.

Real-time gigahertz free-space quantum key distribution within an emulated satellite overpass

Satellite quantum key distribution (SatQKD) intermediated by a trusted satellite in a low-Earth orbit to ground stations along the satellite's path allows remote users to connect securely. To establish a secure connection, a SatQKD session must be conducted to each user over a dynamically changing free-space link, all within just a few hundred seconds. Because of the short time and large losses under which the QKD protocol will be implemented, it has not yet been possible to form a complete key by transmitting all the relevant information required within a single overpass of the satellite. Here, we demonstrate a real-time QKD system that is capable of forming a 4.58-megabit secure key between two nodes within an emulated satellite overpass. We anticipate that our system will set the stage for practical implementations of intercontinental quantum secure communications that can operate over large networks of nodes and enable the secure transmission of data globally.

Practical security analysis of a continuous-variable source-independent quantum random number generator based on heterodyne detection

Heterodyne-based continuous-variable source-independent quantum random number generator (CV-SI-QRNG) can produce true random numbers without any assumptions on source. However, practical implementations always contain imperfections, which will greatly influence the extractable randomness and even open loopholes for eavesdroppers to steal information about the final output. In this work, based on the theoretical model, we systematically analyzed the effects of imperfect implementations on the practical security of heterodyne-based CV-SI-QRNG. The influences of local oscillator (LO) fluctuation under imbalanced heterodyne detection are first analyzed. The simulation results show that the lower bound of extractable randomness will be overestimated without considering the influence of LO fluctuation, which will threaten the practical security of CV-SI-QRNG system. Moreover, we analyze the effects of the degree of imbalance and the magnitude of LO fluctuation on evaluating the extractable randomness. Finally, we investigate the impact of an imperfect phase modulator on the practical security of CV-SI-QRNG and find it will reduce the extractable randomness. Our analysis reveals that one should carefully consider the imperfections in the actual implementations of CV-SI-QRNGs.

Fully Passive Quantum Key Distribution

We propose a fully passive linear optical quantum key distribution (QKD) source that implements both random decoy-state and encoding choices with postselection only, thus eliminating all side channels in active modulators. Our source is general purpose and can be used in, e.g., BB84, the six-state protocol, and reference-frame-independent QKD. It can even potentially be combined with measurement-device-independent QKD to achieve robustness against side channels in both detectors and modulators. We also perform a proof-of-principle experimental source characterization to show its feasibility.

Small-form-factor Gaussian-modulated coherent-state transmitter for CV-QKD using a gain-switched DFB laser

We report a directly modulated distributed feedback laser operating in gain-switching mode for preparing the coherent states required for the Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) protocol. The proposed single-component quantum transmitter design eliminates the need for external modulators, decreasing the complexity of GMCS CV-QKD systems. The experimental results demonstrate a potential asymptotic secret key rate value of 2.63 Mbps over an 11-km fiber link, making the directly modulated GMCS transmitter particularly suitable for metropolitan optical networks where compactness, robustness, and low cost are key desirable features.

Finite-Key Analysis for Quantum Key Distribution with Discrete-Phase Randomization

Quantum key distribution (QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2π, which, however, may be questionable in the experiment. This is particularly the case in the recently proposed twin-field (TF) QKD, which has received a lot of attention since it can increase the key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete-phase randomization instead of continuous randomization. However, a security proof for a QKD protocol with discrete-phase randomization in the finite-key region is still missing. Here, we develop a technique based on conjugate measurement and quantum state distinguishment to analyze the security in this case. Our results show that TF-QKD with a reasonable number of discrete random phases, e.g., 8 phases from {0,π/4,π/2,…,7π/4}, can achieve satisfactory performance. On the other hand, we find the finite-size effects become more notable than before, which implies that more pulses should be emit in this case. More importantly, as a the first proof for TF-QKD with discrete-phase randomization in the finite-key region, our method is also applicable in other QKD protocols.

Random polarization switching in gain-switched VCSELs for quantum random number generation

In this paper, we report an experimental and theoretical study of the random excitation of the linearly polarized modes of a gain-switched VCSEL characterized by having polarization switching under continuous wave operation. We show that equal probability of excitation of both linearly polarized modes can be achieved by adjusting the modulation conditions and the sampling time. Our VCSEL is such that the bistable region associated to the polarization switching is very narrow, indicating that the random process of excitation of the polarizations works independently of the existence of those bistable regions. A characterization of the random polarization switching is performed by analyzing the dependence of the probability of excitation, autocorrelation, and histograms of both polarized signals on the modulation conditions and sampling times. We finally present preliminar results on random number generation using the analyzed system.

Phase diffusion in gain-switched semiconductor lasers for quantum random number generation

In this paper, we report a theoretical and experimental study of the phase diffusion in a gain-switched single-mode semiconductor laser. Our modelling includes nonlinear dependencies of the carrier recombination rate and the semiconductor material gain on the carrier number. Also a comparison with the results obtained with linear models is performed. We focus on the below threshold operation, that is, the regime where most of the phase diffusion occurs in quantum random number generators based on the above mentioned system. Using the extracted parameters for our laser and simple analytical expressions for the laser linewidth, we show that logarithmic material gain and cubic carrier recombination dependence on the carrier number must be considered for a good agreement between experiments and theory. In this way we show that consideration of these nonlinearities is essential for obtaining a good quantitative description of the phase diffusion when using rate equations modelling.

Statistics of the Optical Phase of a Gain-Switched Semiconductor Laser for Fast Quantum Randomness Generation

The statistics of the optical phase of the light emitted by a semiconductor laser diode when subject to periodic modulation of the applied bias current are theoretically analyzed. Numerical simulations of the stochastic rate equations describing the previous system are performed to describe the temporal dependence of the phase statistics. These simulations are performed by considering two cases corresponding to random and deterministic initial conditions. In contrast to the Gaussian character of the phase that has been assumed in previous works, we show that the phase is not distributed as a Gaussian during the initial stages of evolution. We characterize the time it takes the phase to become Gaussian by calculating the dynamical evolution of the kurtosis coefficient of the phase. We show that, under the typical gain-switching with square-wave modulation used for quantum random number generation, quantity is in the ns time scale; that corresponds to the time it takes the system to lose the memory of the distribution of the initial conditions. We compare the standard deviation of the phase obtained with random and deterministic initial conditions to show that their differences become more important as the modulation speed is increased.

Quantum random number generator with discarding-boundary-bin measurement and multi-interval sampling

A quantum random number generator (QRNG) provides a reliable means for the generation of true random numbers. The inherent randomness of the vacuum fluctuations makes the quantum vacuum state a superior source of entropy. However, in practice, the raw sequences of QRNG are inevitably contaminated by classical technical noise, which compromises the security of the QRNG. Min-entropy conditioned on the classical noise is a useful method that can quantify the side-information independent randomness. To improve the extractable randomness from the raw sequences arising from the quantum vacuum-based QRNG, we propose and experimentally demonstrate two approaches, discarding-boundary-bin measurement and multi-interval sampling. The first one increases the conditional min-entropy at a low quantum-to-classical-noise ratio. The latter exploits parallel sampling using multiple analog-to-digital converters (ADCs) and effectively overcomes the finite resolution limit and uniform sampling of a single ADC. The maximum average conditional min-entropy can reach 9.2 per sample when combining these two approaches together in contrast to 6.93 with a single 8-bit ADC.

Homodyne-based quantum random number generator at 2.9 Gbps secure against quantum side-information

Quantum random number generators promise perfectly unpredictable random numbers. A popular approach to quantum random number generation is homodyne measurements of the vacuum state, the ground state of the electro-magnetic field. Here we experimentally implement such a quantum random number generator, and derive a security proof that considers quantum side-information instead of classical side-information only. Based on the assumptions of Gaussianity and stationarity of noise processes, our security analysis furthermore includes correlations between consecutive measurement outcomes due to finite detection bandwidth, as well as analog-to-digital converter imperfections. We characterize our experimental realization by bounding measured parameters of the stochastic model determining the min-entropy of the system’s measurement outcomes, and we demonstrate a real-time generation rate of 2.9 Gbit/s. Our generator follows a trusted, device-dependent, approach. By treating side-information quantum mechanically an important restriction on adversaries is removed, which usually was reserved to semi-device-independent and device-independent schemes.

Security analyses for trusted quantum random number generators usually consider only classical side-information. Here, the authors fill this gap by fully characterising the experimental apparatus of a homodyne-based QRNG, assuming that the vacuum fluctuations and noise are stationary and Gaussian.

Bias-free source-independent quantum random number generator

A bias-free source-independent quantum random number generator scheme based on the measurement of vacuum fluctuation is proposed to realize the effective elimination of system bias and common mode noise introduced by the local oscillator. Optimal parameter settings are derived to avoid the system recording two canonically conjugate quadratures simultaneously in each measurement. In particular, it provides a new approach to investigate the performance difference between measuring two quadratures of equal and unequal intensity. It is experimentally demonstrated that the system supports 4.2 Gbps bias-free source-independent random number generation, where its common mode rejection ratio reaches 61.17 dB. Furthermore, the scheme offers an all-optical method facilitating the integration of source-independent quantum random number generators into compact chips.

Continuous-variable random-number generation from an amplified spontaneous emission light source

An amplified spontaneous emission (ASE) light source using an Er-doped fiber is an ideal random-number source in principle because ASE originates from vacuum fluctuations. Interferometrically measured ASE light directly reflects vacuum fluctuations in phase space; the interferometer does not need to be stabilized because the phase is completely random, and measurable random numbers are a continuous variable because vacuum fluctuations are continuous. These characteristics make the random-number source practical and ideal. Evaluated randomness was sufficiently ideal at the accuracy level of measurements and evaluations.

Quantum noise extraction from the interference of laser pulses in an optical quantum random number generator

We propose a method for quantum noise extraction from the interference of laser pulses with random phase. Our technique is based on the calculation of a parameter, which we called the quantum reduction factor, and which allows for the determination of the contributions of quantum and classical noises with the assumption that classical fluctuations exhibit Gaussian distribution. To the best of our knowledge, the concept of quantum reduction factor is introduced for the first time. We use such an approach to implement the post-processing-free optical quantum random number generator with the random bit generation rate of 2 Gbps.

Random number generation by coherent detection of quantum phase noise

In 2010 Qi et al. [Opt. Lett.35(3), 312 (2010)] demonstrated a random number generator based on the drift of the phase of a laser due to spontaneous emission, The out-of-the-lab implementation of this scheme presents two main drawbacks: it requires a long and highly unbalanced interferometer to generate a random phase with uniform probability distribution, or alternatively, a shorter and slightly unbalanced interferometer that notwithstanding requires active stabilization and does not generate a uniform probability distribution without randomness extraction. Here we demonstrate that making use of the random nature of the phase difference between two independent laser sources and two coherent detectors we can overcome these limitations. The two main advantages of the system demonstrated are: i) it generates a probability distribution of quantum origin which is intrinsically uniform and thus in principle needs no randomness extraction for obtaining a uniform distribution, and ii) the phase is measured with telecom equipment routinely used for high capacity coherent optical communications. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of the lasers. As a by-product of our method, we have obtained images of how phase noise develops with time in a laser. This provides a highly visual alternative way of measuring the coherence time of a laser.

Single Photon Randomness based on a Defect Center in Diamond

The prototype of a quantum random number generator is a single photon which impinges onto a beam splitter and is then detected by single photon detectors at one of the two output paths. Prior to detection, the photon is in a quantum mechanical superposition state of the two possible outcomes with –ideally– equal amplitudes until its position is determined by measurement. When the two output modes are observed by a single photon detector, the generated clicks can be interpreted as ones and zeros – and a raw random bit stream is obtained. Here we implement such a random bit generator based on single photons from a defect center in diamond. We investigate the single photon emission of the defect center by an anti-bunching measurement. This certifies the “quantumness” of the supplied photonic input state, while the random “decision” is still based on the vacuum fluctuations at the open port of the beam-splitter. Technical limitations, such as intensity fluctuations, mechanical drift, and bias are discussed. A number of ways to suppress such unwanted effects, and an a priori entropy estimation are presented. The single photon nature allows for a characterization of the non-classicality of the source, and allows to determine a background fraction. Due to the NV-center’s superior stability and optical properties, we can operate the generator under ambient conditions around the clock. We present a true 24/7 operation of the implemented random bit generator.

6 Gbps real-time optical quantum random number generator based on vacuum fluctuation

We demonstrate a 6 Gbps real-time optical quantum random number generator by measuring vacuum fluctuation. To address the common problem that speed gap exists between fast randomness generation and slow randomness extraction in most high-speed real-time quantum random number generator systems, we present an optimized extraction algorithm based on parallel implementation of Toeplitz hashing to reduce the influence of classical noise due to the imperfection of devices. Notably, the real-time rate of randomness extraction we have achieved reaches the highest speed of 12 Gbps by occupying less computing resources, and the algorithm has the ability to support hundreds of Gbps randomness extraction. By assuming that the eavesdropper with complete knowledge of the classical noise, our generator has a randomness generation speed of 6.83 Gbps and this supports the generation of 6 Gbps information-theoretically provable quantum random numbers, which are output in real-time through peripheral component interconnect express interface.

Interferometric photodetection in silicon photonics for phase diffusion quantum entropy sources

We report the interferometric photodetection of a phase-diffusion quantum entropy source in a silicon photonics chip. The device uses efficient and robust single-laser accelerated phase diffusion methods, and implements the unbalanced Mach-Zehnder interferometer with optimized splitting ratio and photodetection, in a 0.5 mm×1 mm footprint. We demonstrate Gbps raw entropy-generation rates in a technology compatible with conventional CMOS fabrication techniques.

Generation of random on-off modulation pulses by optically injecting a gain-switched Fabry-Pérot semiconductor laser with a dual-mode injection for random-modulation pulsed lidar applications

We study the generation of random on-off modulation pulses by optically injecting a gain-switched Fabry-Pérot semiconductor laser with a dual-mode injection for random-modulation pulsed lidar applications. In the dual-mode injection scheme proposed, the first master laser (ML1) injecting on a resonant sidemode of the gain-switched slave laser (SL) randomly locks such injected sidemode and suppresses the output pulses in the center mode through gain-competition. The second master laser (ML2) injecting on the center mode then stabilizes and enhances the output pulses to have equal amplitudes suitable for digital threshold detection and time-correlated single photon counting. Under different injection conditions, we identify dynamical states including unlocked, stable locking, bistable, and instability. By operating the laser in the bistable states randomly switching between the unlocked and stable locking states, we successfully generate random on-off modulation pulses without employing any digital circuits or external modulators. We analyze the signal-to-noise ratio (SNR) and detection probability of the proposed scheme to show its feasibility in random-modulation pulsed lidar applications. Moreover, we study its anti-interference capability by adding interference from additional channels with similar modulated pulses. We show that, with injection strengths of 0.418 and 0.038 from the ML1 and ML2 and a correlation length T_c = 90 µs, a detection probability of 1 can be readily achieved even under the interference from more than 49 additional channels.

Testing the photon-number statistics of a quantum key distribution light source

A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source's photon statistics and use it in the estimation of a quantum key distribution system's key rate. This promises to be a useful tool for the certification of quantum-related technologies.

Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip

Random numbers are a fundamental resource in science and technology. Among the different approaches to generating them, random numbers created by exploiting the laws of quantum mechanics have proven to be reliable and can be produced at enough rates for their practical use. While these demonstrations have shown very good performance, most of the implementations using free-space and fibre optics suffer from limitations due to their size, which strongly limits their practical use. Here we report a quantum random number generator based on phase fluctuations from a diode laser, where the other required optical components are integrated on a mm-scale monolithic silicon-on-insulator chip. The post-processing reported in this experiment is performed via software. However, our physical device shows the potential of operation at generation rates in the Gbps regime. Considering the device's size, its simple, robust and low power operation, and the rapid industrial uptake of silicon photonics, we foresee the widespread integration of the reported design in more complex systems.

Programmable quantum random number generator without postprocessing

We demonstrate a viable source of unbiased quantum random numbers whose statistical properties can be arbitrarily programmed without the need for any postprocessing such as randomness distillation or distribution transformation. It is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. We show that quantum random numbers can be created directly in customized probability distributions and pass all randomness tests of the NIST and Dieharder test suites without any randomness extraction. The min-entropies of such generated random numbers are measured close to the theoretical limits, indicating their near-ideal statistics and ultrahigh purity. Easy to implement and arbitrarily programmable, this technique can find versatile uses in a multitude of data analysis areas.

Randomness in quantum mechanics: philosophy, physics and technology

This progress report covers recent developments in the area of quantum randomness, which is an extraordinarily interdisciplinary area that belongs not only to physics, but also to philosophy, mathematics, computer science, and technology. For this reason the article contains three parts that will be essentially devoted to different aspects of quantum randomness, and even directed, although not restricted, to various audiences: a philosophical part, a physical part, and a technological part. For these reasons the article is written on an elementary level, combining simple and non-technical descriptions with a concise review of more advanced results. In this way readers of various provenances will be able to gain while reading the article.

True randomness from an incoherent source

Quantum random number generators (QRNGs) harness the intrinsic randomness in measurement processes: the measurement outputs are truly random, given the input state is a superposition of the eigenstates of the measurement operators. In the case of trusted devices, true randomness could be generated from a mixed state ρ so long as the system entangled with ρ is well protected. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state using an optical homodyne detector. By mixing the output of a broadband amplified spontaneous emission (ASE) source with a single mode local oscillator (LO) at a beam splitter and performing differential photo-detection, we can selectively detect the quadrature fluctuation of a single mode output of the ASE source, thanks to the filtering function of the LO. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise has been observed, suggesting this scheme can tolerate much higher detector noise in comparison with QRNGs based on measuring the vacuum noise. The high quality of this entropy source is evidenced by the small correlation coefficients of the acquired data. A Toeplitz-hashing extractor is applied to generate unbiased random bits from the Gaussian distributed raw data, achieving an efficiency of 5.12 bits per sample. The output of the Toeplitz extractor successfully passes all the NIST statistical tests for random numbers.

Proof-of-principle implementation of a quantum random number generator with independent devices and a dimension witness

The random number is a paramount issue in modern science. How to estimate the genuine randomness of the data generated by a given device is a central problem. Lunghi et al. proposed a self-testing quantum random number generator from a prepare-and-measure scenario with independent devices. Based on this Letter, Han et al. proposed a more efficient method (Han16 protocol for short) to estimate the genuine randomness. Here we report a proof-of-principle realization of the Han16 protocol with a HSPS. The experimental results demonstrate that the Han16 protocol almost doubles the generation rate of the quantum random number with regard to the previous protocol. In addition, the results of the experiment show that the Han16 protocol is practical, and the experimental device can tolerate loss and noise.

Quantum key distribution with hacking countermeasures and long term field trial

Quantum key distribution’s (QKD’s) central and unique claim is information theoretic security. However there is an increasing understanding that the security of a QKD system relies not only on theoretical security proofs, but also on how closely the physical system matches the theoretical models and prevents attacks due to discrepancies. These side channel or hacking attacks exploit physical devices which do not necessarily behave precisely as the theory expects. As such there is a need for QKD systems to be demonstrated to provide security both in the theoretical and physical implementation. We report here a QKD system designed with this goal in mind, providing a more resilient target against possible hacking attacks including Trojan horse, detector blinding, phase randomisation and photon number splitting attacks. The QKD system was installed into a 45 km link of a metropolitan telecom network for a 2.5 month period, during which time the system operated continuously and distributed 1.33 Tbits of secure key data with a stable secure key rate over 200 kbit/s. In addition security is demonstrated against coherent attacks that are more general than the collective class of attacks usually considered.

Random Number Generation with Cosmic Photons

Random numbers are indispensable for a variety of applications ranging from testing physics foundations to information encryption. In particular, nonlocality test provide strong evidence for our current understanding of nature-quantum mechanics. All the random number generators (RNGs) used for the existing tests are constructed locally, making the test results vulnerable to the freedom-of-choice loophole. We report an experimental realization of RNGs based on the arrival time of cosmic photons. The measurement outcomes (raw data) pass the standard NIST statistical test suite. We present a realistic design to employ these RNGs in a Bell test experiment, which addresses the freedom-of-choice loophole.

Quantum random number generator using a microresonator-based Kerr oscillator

We demonstrate an all-optical quantum random number generator using a dual-pumped degenerate optical parametric oscillator in a silicon nitride microresonator. The frequency-degenerate bi-phase state output is realized using parametric four-wave mixing in the normal group-velocity dispersion regime with two nondegenerate pumps. We achieve a random number generation rate of 2 MHz and verify the randomness of our output using the National Institute of Standards and Technology Statistical Test Suite. The scheme offers potential for a chip-scale random number generator with gigahertz generation rates and no postprocessing.

Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis

The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682–686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator.

Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons

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.

Generation of Fresh and Pure Random Numbers for Loophole-Free Bell Tests

We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below 10^{-5} and strong metrological randomness assurances. This randomness generation strategy satisfies the stringent requirements for unpredictable basis choices in current "loophole-free Bell tests" of local realism [Hensen et al., Nature (London) 526, 682 (2015); Giustina et al., this issue, Phys. Rev. Lett. 115, 250401 (2015); Shalm et al., preceding Letter, Phys. Rev. Lett. 115, 250402 (2015)].

An On-Demand Optical Quantum Random Number Generator with In-Future Action and Ultra-Fast Response

Random numbers are essential for our modern information based society e.g. in cryptography. Unlike frequently used pseudo-random generators, physical random number generators do not depend on complex algorithms but rather on a physicsal process to provide true randomness. Quantum random number generators (QRNG) do rely on a process, wich can be described by a probabilistic theory only, even in principle. Here we present a conceptualy simple implementation, which offers a 100% efficiency of producing a random bit upon a request and simultaneously exhibits an ultra low latency. A careful technical and statistical analysis demonstrates its robustness against imperfections of the actual implemented technology and enables to quickly estimate randomness of very long sequences. Generated random numbers pass standard statistical tests without any post-processing. The setup described, as well as the theory presented here, demonstrate the maturity and overall understanding of the technology.

Modulation instability in a highly nonlinear fiber for discrete-time pulsed random bit generation

A simple yet high-speed scheme by utilizing modulation instability (MI) on the discrete-time generation of random bits is proposed and demonstrated experimentally. We develop MI pulses by pumping a highly nonlinear fiber in the anomalous dispersion regime using a mode-locked laser. MI pulses contain fluctuating pulse-to-pulse variations of peak intensities for extraction into random bits. At a repetition rate of 10 GHz, 5 bits are extracted from each pulse in generating random bits at 50 Gbps, as verified by the National Institute of Standards and Technology test suite.

Self-testing quantum random number generator

The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices.