Self-testing and Semi-Device Independent protocols are becoming the preferred choice for quantum technologies, being able to certify their quantum nature with few assumptions and simple experimental implementations. In particular for Quantum Random Number Generators the possibility of monitoring in real time the entropy of the source only by measuring the input/output statistics is a characteristic that no other classical system could provide. The cost of this new possibility is not necessarily increased complexity and reduced performance. Indeed, here we show that with a simple optical setup consisting of commercially available components, a high bit generation rate can be achieved. We manage to certify 145.5~MHz of quantum random bit generation rate.
We demonstrate that different kind of mesoscopic quantum states of light can be efficiently generated from a simple iterative scheme using homodyne heralding. These states exhibit strong non-classical features, and are of great interest for many applications such as quantum error-correcting codes or fundamental testings. On this basis we propose a protocol allowing a large loophole-free violation of a CHSH-type Bell inequality with a remarkable robustness to line losses.
Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between measuring photon numbers and field quadratures. We combine a quantum signal with a coherent state on a balanced beam splitter and detect light at both output ports using photon-number-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution of the signal as we increase the coheren…
A single quantum particle can be described by a wavefunction that spreads over arbitrarily large distances, but it is never detected in two (or more) places. This strange phenomenon is explained in quantum theory by what Einstein repudiated as "spooky action at a distance": the instantaneous nonlocal collapse of the wavefunction to wherever the particle is detected. We demonstrate this single-particle spooky action, for the first time with no efficiency loophole, by splitting a single photon between two laboratories and experimentally testing if the choice of measurement in one lab really caus…
In the last decade, there has been remarkable progress on the practical integration of on-chip quantum photonic devices yet quantum state generators remain an outstanding challenge. Simultaneously, the quantum-dot photonic-crystal-resonator platform has demonstrated a versatility for creating nonclassical light with tunable quantum statistics, thanks to a newly discovered self-homodyning interferometric effect that preferentially selects the quantum light over the classical light when using an optimally tuned Fano resonance. In this work, we propose a general structure for the cavity quantum e…
We show that arbitrary functions of continuous variables, e.g. position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimising these functions, we obtain more robust violations of local causality than obtained previously. We analytically calculate the optimal function and include the effect of nonideal detectors and noise, revealing that optimized functional inequalities are resistant to standard forms of decoherence. These inequalities could allow a loophole-free Bell test with efficient homodyne detection.
Balanced homodyne detector (BHD) that can measure the field quadratures of coherent states has been widely used in a range of quantum information technologies. Generally, the BHD tends to suffer from narrow bands and an expanding bandwidth behavior usually traps into a compromise with the gain, electronic noise, and quantum to classical noise ratio, etc. In this paper, we design and construct a wideband BHD based on radio frequency and integrated circuit technology. Our BHD shows bandwidth behavior up to 1.2 GHz and its quantum to classical noise ratio is around 18 dB. Simultaneously, the BHD …
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；University of Oxford（牛津大学）
Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task with current state-of-the-art techniques becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a quantum harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to optical homodyne tomography and show it t…
We present a scheme for a self-testing quantum random number generator. Compared to the fully device-independent model, our scheme requires an extra natural assumption, namely that the mean energy per signal is bounded. The scheme is self-testing, as it allows the user to verify in real-time the correct functioning of the setup, hence guaranteeing the continuous generation of certified random bits. Based on a prepare-and-measure setup, our scheme is practical, and we implement it using only off-the-shelf optical components. The randomness generation rate is 1.25 Mbits/s, comparable to commerci…
We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. …
For the first time, the theory and practical realization of a broadband quantum noise generator based on original integrated optical beam splitter in the form of a Mach-Zehnder interferometer is demonstrated. The beam splitter with a double output, made on a lithium niobate substrate, provided accurate electro-optical balancing of the homodyne quantum noise detection circuit. According to our knowledge, the experimentally obtained excess of quantum noise over classical noise by 12 dB in the frequency band over 4 GHz, which is the best parameters of quantum noise generators known from the liter…
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
The study of light-matter interaction at the quantum scale has been enabled by the cavity quantum electrodynamics (CQED) architecture, in which a quantum two-level system strongly couples to a single cavity mode. Originally implemented with atoms in optical cavities, CQED effects are now also observed with artificial atoms in solid-state environments. Such realizations of these systems exhibit fast dynamics, which makes them attractive candidates for devices including modulators and sources in high-throughput communications. However, these systems possess large photon out-coupling rates that o…
Quantum random number generators (QRNGs) are able to generate numbers that are certifiably random, even to an agent who holds some side-information. Such systems typically require that the elements being used are precisely calibrated and validly certified for a credible security analysis. However, this can be experimentally challenging and result in potential side-channels which could compromise the security of the QRNG. In this work, we propose, design and experimentally demonstrate a QRNG protocol that completely removes the calibration requirement for the measurement device. Moreover, our p…
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 illustr…
In a Bayesian analysis, the likelihood that specific candidate parameters govern the evolution of a quantum system are conditioned on the outcome of measurements which, in turn, cause measurement backaction on the state of the system [M. Tsang, Phys. Rev. Lett. 108, 170502 (2012)]. Specializing to the distinction of two candidate hypotheses, we study the achievements of continuous monitoring of the radiation emitted by a quantum system followed by an optimal projective measurement on its conditioned final state. Our study of the radiative decay of a driven two-level system shows an intricate i…
Authors develop new nonparametric methods for verification and monitoring for quantum randomness based on the ranged correlation function (RCF) and a sequence of the ranged amplitudes (SRA). We carried out RCF-analysis of different topology subsamples from raw data of the prototype of a quantum random number generator on homodyne detection. It is shown that in the real system there are weak local regression relations, for which it is possible to introduce a robust criterion of significance, and also precise SRA-identification of long samples statistics is made. The obtained results extend the …
Phase-randomized optical homodyne detection is a well-known technique for performing quantum state tomography. So far, it has been mainly considered a sophisticated tool for laboratory experiments but unsuitable for practical applications. In this work, we change the perspective and employ this technique to set up a practical continuous-variable quantum random number generator. We exploit a phase-randomized local oscillator realized with a gain-switched laser to bound the min-entropy and extract true randomness from a completely uncharacterized input, potentially controlled by a malicious adve…
Quantum random number generation exploits inherent randomness of quantum mechanical processes and measurements. Real-time generation rate of quantum random numbers is usually limited by electronic bandwidth and data processing rates. Here we use a multiplexing scheme to create a fast real-time quantum random number generator based on continuous variable vacuum fluctuations. Multiple sideband frequency modes of a quantum vacuum state within a homodyne detection bandwidth are concurrently extracted as the randomness source. Parallel post-processing of raw data from three sub-entropy sources is r…
A quantum random-number generator (QRNG) can theoretically generate unpredictable random numbers with perfect devices and is an ideal and secure source of random numbers for cryptography. However, the practical implementations always contain imperfections, which will greatly influence the randomness of the final output and even open loopholes to eavesdroppers. Recently, Thewes et al. experimentally demonstrated a continuous-variable eavesdropping attack, based on heterodyne detection, on a trusted continuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like in many other practical con…
Random numbers are a fundamental ingredient for many applications including simulation, modelling and cryptography. Sound random numbers should be independent and uniformly distributed. Moreover, for cryptographic applications they should also be unpredictable. We demonstrate a real-time self-testing source independent quantum random number generator (QRNG) that uses squeezed light as source. We generate secure random numbers by measuring the quadratures of the electromagnetic field without making any assumptions on the source; only the detection device is trusted. We use a homodyne detection …
Quantum random number generators (QRNGs) can produce true random numbers. Yet, the two most important QRNG parameters highly desired for practical applications, i.e., speed and size, have to be compromised during implementations. Here, we present the fastest and miniaturized QRNG with a record real-time output rate as high as 18.8 Gbps by combining a photonic integrated chip and the technology of optimized randomness extraction. We assemble the photonic integrated circuit designed for vacuum state QRNG implementation, InGaAs homodyne detector and high-bandwidth transimpedance amplifier into a …
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models as approximation. A necessary condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov process which are based upon the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation fo…
Fast secure random number generation is essential for high-speed encrypted communication, and is the backbone of information security. Generation of truly random numbers depends on the intrinsic randomness of the process used and is usually limited by electronic bandwidth and signal processing data rates. Here we use a multiplexing scheme to create a fast quantum random number generator structurally tailored to encryption for distributed computing, and high bit-rate data transfer. We use vacuum fluctuations measured by seven homodyne detectors as quantum randomness sources, multiplexed using a…
Continuous-variable quantum cryptographic systems, including random number generation and key distribution, are often based on coherent detection. The essence of the security analysis lies in the randomness quantification. Previous analyses employ a semi-quantum picture, where the strong local oscillator limit is assumed. Here, we investigate the randomness of homodyne detection in a full quantum scenario by accounting for the shot noise in the local oscillator, which requires us to develop randomness measures in the infinite-dimensional scenario. Similar to the finite-dimensional case, our in…
Randomness is a very important resource for cryptography, algorithms, and scientific simulations. Since all classical processes are considered to be intrinsically deterministic, we must build quantum random number generators which utilize quantum processes to generate true randomness. Quantum random number generators have been realized in different quantum systems, including quantum optical systems, and trapped ions. Here we present a proof-of-concept random number generator based on a nuclear spin system for the first time. The state preparation and measurements are performed with high-fideli…
Quantum random number generators (QRNG) are based on the naturally random measurement results performed on individual quantum systems. Here, we demonstrate a branching-path photonic QRNG implemented with a Sagnac interferometer with a tunable splitting ratio. The fine-tuning of the splitting ratio allows us to maximize the entropy of the generated sequence of random numbers and effectively compensate for tolerances in the components. By producing single-photons from attenuated telecom laser pulses, and employing commercially-available components we are able to generate a sequence of more than …
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow a 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 characterise a light source's photon statistics and use it in the …
Quantum mechanics provides means of generating genuine randomness that is impossible with deterministic classical processes. Remarkably, the unpredictability of randomness can be certified in a self-testing manner that is independent of implementation devices. Here, we present an experimental demonstration of self-testing quantum random number generation based on an detection-loophole free Bell test with entangled photons. In the randomness analysis, without the assumption of independent identical distribution, we consider the worst case scenario that the adversary launches the most powerful a…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this revi…
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in O (k^{2/3}). The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of Omega(k^{2/3}), we give a reduction from a special case of Element Distinctness to our problem. Along the way, we prove the optimality of the algori…
One of the main challenges in the Variational Quantum Eigensolver (VQE) framework is construction of the unitary transformation. The dimensionality of the space for unitary rotations of $N$ qubits is $4^N-1$, which makes the choice of a polynomial subset of generators exponentially difficult process. Moreover, due to non-commutativity of generators, the order in which they are used strongly affects results. Choosing the optimal order in a particular subset of generators requires testing the factorial number of combinations. We propose an approach based on the Lie algebra - Lie group connection…
We propose a practical scheme to use photons from causally disconnected cosmic sources to set the detectors in an experimental test of Bell's inequality. In current experiments, with settings determined by quantum random number generators, only a small amount of correlation between detector settings and local hidden variables, established less than a millisecond before each experiment, would suffice to mimic the predictions of quantum mechanics. By setting the detectors using pairs of quasars or patches of the cosmic microwave background, observed violations of Bell's inequality would require …
