Any characterization of a single-photon source is not complete without specifying its second-order degree of coherence, i.e., its $g^{(2)}$ function. An accurate measurement of such coherence functions commonly requires high-precision single-photon detectors, in whose absence, only time-averaged measurements are possible. It is not clear, however, how the resulting time-averaged quantities can be used to properly characterize the source. In this paper, we investigate this issue for a heralded source of single photons that relies on continuous-wave parametric down-conversion. By accounting for major shortcomings of the source and the detectors--i.e., the multiple-photon emissions of the source, the time resolution of photodetectors, and our chosen width of coincidence window--our theory enables us to infer the true source properties from imperfect measurements. Our theoretical results are corroborated by an experimental demonstration using a PPKTP crystal pumped by a blue laser, that results in a single-photon generation rate about 1.2 millions per second per milliwatt of pump power. This work takes an important step toward the standardization of such heralded single-photon sources.
We propose a setup for a heralded, i.e. announced generation of a pure single-photon state given two imperfect sources whose outputs are represented by mixtures of the single-photon Fock state $\ket{1}$ with the vacuum $\ket{0}$. Our purification scheme uses beam splitters, photodetection and a two-photon-absorbing medium. The admixture of the vacuum is fully eliminated. We discuss two potential realizations of the scheme.
Based on the signal and idler photon pairs produced in a piece of high nonlinear fiber by a pulsed pump, we characterize the heralded single photon source from both the theoretical and experimental aspects. In the theory model, started from the derived expression of Bogoliubov transformation for a broadband pulsed pump, the second-order intensity correlation function $g_c^{(2)}(0)$, heralding efficiency $H$, indistinguishability and brightness of the heralded single photons as a function of source parameters are analyzed and discussed. In the experiments, using several kinds of combinations of…
Quantum Key Distribution (QKD) is one of the most important aspects of quantum cryptography. Using laws of quantum mechanics as the basis for security, the key distribution process is made information theoretically secure in QKD. With the advancement and commercialization of QKD, an end-to-end QKD simulation software is required that can include experimental imperfections. Software of this kind will ensure that resources are invested only after prior performance analysis, and is faithful to experimental capacities and limitations. In this work, we introduce our QKD simulation toolkit qkdSim, w…
Realistic single-photon sources do not generate single photons with certainty. Instead they produce statistical mixtures of photons in Fock states $\ket{1}$ and vacuum (noise). We describe how to eliminate the noise in the output of the sources by means of another noisy source or a coherent state and cross phase modulation (XPM). We present a scheme which announces the production of pure single photons and thus eliminates the vacuum contribution. This is done by verifying a XPM related phase shift with a Mach-Zehnder interferometer.
We examine the behavior of non-Gaussian states of light under the action of probabilistic noiseless amplification and attenuation. Surprisingly, we find that the mean field amplitude may decrease in the process of noiseless amplification -- or increase in the process of noiseless attenuation, a counterintuitive effect that Gaussian states cannot exhibit. This striking phenomenon could be tested with experimentally accessible non-Gaussian states, such as single-photon added coherent states. We propose an experimental scheme, which is robust with respect to the major experimental imperfections s…
We analyze theoretically performance of four-state quantum key distribution protocols implemented with a realistic heralded single-photon source. The analysis assumes a noisy model for the detector heralding generation of individual photons via spontaneous parametric down-conversion, including dark counts and imperfect photon number resolution. We identify characteristics of the heralding detector that defines the attainable cryptographic key rate and the maximum secure distance. Approximate analytical formulas are applied to multiplexed detection and compared with results of numerical calcula…
We propose a realistic protocol for the preparation and readout of mechanical Bell states in an optomechanical system. The proposal relies on parameters characterizing a photonic crystal cavity mode, coupled to two localized flexural modes of the structure, but equally applies to other optomechanical systems in the same parameter range. The nonclassical states are heralded via optical postselection and revealed in specific interference patterns characterizing the emission at the cavity frequency.
We perform experimental quantum polarimetry using a heralded single photon to analyze the optical activity of linearly polarized light traversing a chiral medium. Three kinds of estimators are considered to estimate the concentrations of sucrose solutions from measuring the rotation angle of the linear polarization of the output photons. Through repetition of independent and identical measurements performed for each individual scheme and different concentration sucrose solutions, we compare the estimation uncertainty among the three schemes. The results are also compared to classical benchmark…
High visibility on-chip quantum interference among indistinguishable single-photons from multiples sources is a key prerequisite for integrated linear optical quantum computing. Resonant enhancement in micro-ring resonators naturally enables brighter, purer and more indistinguishable single-photon production without any tight spectral filtering. The indistinguishability of heralded single-photons from multiple micro-ring resonators has not been measured in any photonic platform. Here, we report on-chip indistinguishability measurements of heralded single-photons generated from independent micr…
When building a parametric downconversion photon-pair source with spectrally separable photons, e.g. for making high-purity heralded single photons, two practical issues must be accounted for: the design of the experiment, and its characterization. To address experiment design, we study the impact on spectral separability of realistic (sech shaped and chirped) pump fields, realistic nonlinear crystals with fabrication imperfections, and undesirable PDC generation far from the central PMF peak coming from nonlinearity shaping methods. To address experiment characterization, we study the effect …
Hyperentangled Bell-state analysis (HBSA) is critical for high-capacity quantum communication. Here we design two effective schemes for error-heralded deterministic generation and self-assisted complete analysis of hyperentangled Bell states for two-photon systems in both the polarization and spatial-mode degrees of freedom, assisted by single-sided quantum-dot-cavity systems. We construct an error-heralded block with a singly charged quantum dot inside a single-sided optical microcavity, two circular polarization beam splitters, one half-wave plate, and one single-photon detector, in which th…
We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive…
We present a quantum repeater scheme based on the recently proposed qubit amplifier [N. Gisin, S. Pironio and N. Sangouard, Phys. Rev. Lett. 105, 070501 (2010)]. It relies on a on-demand entangled-photon pair source which uses on-demand single-photon sources, linear optical elements and atomic ensembles. Interestingly, the imperfections affecting the states created from this source, caused e.g. by detectors with non-unit efficiencies, are systematically purified from an entanglement swapping operation based on a two-photon detection. This allows the distribution of entanglement over very long …
Due to their strict photon-number correlation, the twin beams produced in parametric down-conversion (PDC) work well for heralded state generation. Often, however, this state manipulation is distorted by the optical losses in the herald and by the higher photon-number contributions inevitable in the PDC process. In order to find feasible figures of merit for characterizing the heralded states, we investigate their normalized factorial moments of the photon number that can be accessed regardless of the optical losses in the detection. We then perform a measurement of the joint photon statistics…
We introduce the thermal-difference states (TDS), a three-parameter family of single-mode non-Gaussian bosonic states whose density operator is a weighted difference of two thermal states. We show that the states of "heralded photons" generated via parametric down-conversion (PDC) are precisely those among the TDS that are nonclassical, meaning they have a negative $P$-function. The three parameters correspond in that context to the initial brightness of PDC and the transmittances, characterizing the linear loss in the signal and the idler channels. At low initial brightness and unit transmitt…
Quantum repeater is one of the important building blocks for long distance quantum communication network. The previous quantum repeaters based on atomic ensembles and linear optical elements can only be performed with a maximal success probability of 1/2 during the entanglement creation and entanglement swapping procedures. Meanwhile, the polarization noise during the entanglement distribution process is harmful to the entangled channel created. Here we introduce a general interface between a polarized photon and an atomic ensemble trapped in a single-sided optical cavity, and with which we pr…
To realize the practical implementation of device-independent quantum key distribution~(DIQKD), the main difficulty is that its security relies on the detection-loophole-free violation of the Clauser-Horne-Shimony-Holt~(CHSH) inequality, i.e. the CHSH value $S>2$, which is easily destroyed by the loss in transmission channels. One of the simplest methods to circumvent it is to utilize the entanglement swapping relay~(ESR). Here, we propose and experimentally test an improved version of the heralded nonlocality amplifier protocol based on the ESR, and numerically show that our scheme is much mo…
Heralded entangled state generation enhanced by photon addition and subtraction
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学中科院量子信息与量子物理卓越创新中心）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
本文提出了一种基于高斯源的 heralded 熵生成方案，通过结合单模压缩、线性干涉仪和辅助模式的条件光子数测量，实现双轨编码的 Bell、GHZ 和 W 状态生成，并优化参数以提高生成效率和保真度。
Loss is a critical roadblock to achieving photonic quantum-enhanced technologies. We explore a modular platform for implementing integrated photonics experiments and consider the effects of loss at different stages of these experiments, including state preparation, manipulation and measurement. We frame our discussion mainly in the context of quantum sensing and focus particularly on the use of loss-tolerant Holland-Burnett states for optical phase estimation. In particular, we discuss spontaneous four-wave mixing in standard birefringent fibre as a source of pure, heralded single photons and …
Scalable photonic quantum technologies require highly efficient sources of single photons on demand. Although much progress has been done in the field within the last decade, the requirements impose stringent conditions on the efficiency of such devices. One of the most promising approaches is to multiplex a single or several heralded photon sources into temporal modes. In this work we analyze a specific proposal to synchronize photons from a continuous source with an external reference clock using imperfect optical switches, which necessarily degrade the ideal behavior of the devised arrangem…
Single photons provide excellent quantum information carriers, but current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed single photons, while linear-optics gates are inherently probabilistic. Here, we introduce a deterministic scheme for photonic quantum information. Our single, versatile process---coherent photon conversion---provides a full suite of photonic quantum processing tools, from creating high-quality heralded single- and multiphoton states free of higher-order imperfections to implementing d…
We report the first experimental demonstration of an optical controlled-NOT gate constructed entirely in fibre. We operate the gate using two heralded optical fibre single photon sources and find an average logical fidelity of 90% and an average process fidelity of 0.83<F<0.91. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity.
Generating quantum entanglement is not only an important scientific endeavor, but will be essential to realizing quantum-enhanced technologies, in particular, quantum-enhanced measurements with precision beyond classical limits. We investigate the heralded generation of multiphoton entanglement for quantum metrology using a reconfigurable integrated waveguide device in which projective measurement of auxiliary photons heralds the generation of path-entangled states. We use four and six-photon inputs, to analyze the heralding process of two- and four-photon NOON states-a superposition of N phot…
We experimentally investigate a method of directly characterizing the photon number distribution of nonclassical light beams that is tolerant to losses and makes use only of standard binary detectors. This is achieved in a single measurement by calibrating the detector using some small amount of prior information about the source. We demonstrate the technique on a freely propagating heralded two-photon number state created by conditional detection of a two-mode squeezed state generated by a parametric downconverter.
Deterministic generation of single photons is essential for many quantum information technologies. A bulk optical nonlinearity emitting a photon pair, where the measurement of one of the photons heralds the presence of the other, is commonly used with the caveat that the single-photon emission rate is constrained due to a trade-off between multiphoton events and pair emission rate. Using an efficient and low noise photon-number-resolving superconducting nanowire detector we herald, in real time, a single photon at telecommunication wavelength. We perform a second-order photon correlation $g^{2…
We generalize measurement-device-independent quantum key distribution [ H.-K. Lo, M. Curty, and B. Qi, Phys. Rev. Lett. 108, 130503 (2012) ] to the scenario where the Bell-state measurement station contains also heralded quantum memories. We find analytical formulas, in terms of device imperfections, for all quantities entering in the secret key rates, i.e., the quantum bit error rate and the repeater rate. We assume either single-photon sources or weak coherent pulse sources plus decoy states. We show that it is possible to significantly outperform the original proposal, even in presence of d…
Decoy state and purification protocols for superior quantum key distribution with imperfect quantum-dot based single photon sources: Theory and Experiment
The desire to understand the interaction between light and matter has stimulated centuries of research, leading to technological achievements that have shaped our world. One contemporary frontier of research into light-matter interaction considers regimes where quantum effects dominate. By understanding and manipulating these quantum effects, a vast array of new quantum-enhanced technologies become accessible. In this thesis, I explore and analyze fundamental components and processes for quantum optical devices with a focus on solid-state quantum systems. This includes indistinguishable single…
We present improved results and more general results for the decoy-state measurement device independent quantum key distribution (MDI-QKD) where the intensities of all 3 pulses can be non-zero. We present a more tightened explicit formula for the lower bound of the yield of two single-photon pulses for this generalized 3-intensity protocol, which can be applied to the recently proposed MDI-QKD with imperfect single-photon sources such as the coherent states or the heralded states from the parametric down-conversion. We strictly prove that our result is better than the prior art result. With th…
Given a suitably large and well connected (complex) graph state, any quantum algorithm can be implemented purely through local measurements on the individual qubits. Measurements can also be used to create the graph state: Path erasure techniques allow one to entangle multiple qubits by determining only global properties of the qubits. Here, this powerful approach is extended by demonstrating that even imperfect path erasure can produce the required graph states with high efficiency. By characterizing the degree of error in each path erasure attempt, one can subsume the resulting imperfect ent…
Here we argue that the probability that a given source produces exactly a single photon is a natural quantity to benchmark single-photon sources as it certifies the absence of multi-photon components and quantifies the efficiency simultaneously. Moreover, this probability can be bounded simply from an auto-correlation measurement -- a balanced beam splitter and two photon detectors. Such a bound gives access to various non-classicality witnesses that can be used to certify and quantify Wigner-negativity, in addition to non-Gaussianity and P-negativity of the state produced by the source. We pr…
We study the operation of linear optics schemes for entanglement distribution based on nonlocal photon subtraction when input states, produced by imperfect single-photon sources, exhibit both vacuum and multiphoton contributions. Two models for realistic photon statistics with radically different properties of the multiphoton "tail" are considered. The first model assumes occasional emission of double photons and linear attenuation, while the second one is motivated by heralded sources utilizing spontaneous parametric down-conversion. We find conditions for the photon statistics that guarantee…
The experimental characterization of multi-photon quantum interference effects in optical networks is essential in many applications of photonic quantum technologies, which include quantum computing and quantum communication as two prominent examples. However, such characterization often requires technologies which are beyond our current experimental capabilities, and today's methods suffer from errors due to the use of imperfect sources and photodetectors. In this paper, we introduce a simple experimental technique to characterise multi-photon quantum interference by means of practical laser …
We demonstrate a new technique for characterizing two-photon quantum states based on joint temporal correlation measurements using time resolved single photon detection by femtosecond upconversion. We measure for the first time the joint temporal density of a two-photon entangled state, showing clearly the time anti-correlation of the coincident-frequency entangled photon pair generated by ultrafast spontaneous parametric down-conversion under extended phase-matching conditions. The new technique enables us to manipulate the frequency entanglement by varying the down-conversion pump bandwidth …
We demonstrate a method to determine the spectral purity of single photons. The technique is based on the Hong-Ou-Mandel (HOM) interference between a single photon state and a suitably prepared coherent field. We show that the temporal width of the HOM dip is not only related to reciprocal of the spectral width but also to the underlying quantum coherence. Therefore, by measuring the width of both the HOM dip and the spectrum one can directly quantify the degree of spectral purity. The distinct advantage of our proposal is that it obviates the need for perfect mode matching, since it does not …
We study the measurement device independent quantum key distribution (MDIQKD) in practice with limited resource, when there are only 3 different states in implementing the decoy-state method and when there are basis dependent coding errors. We present general formulas for the decoy-state method for two-pulse sources with 3 different states, which can be applied to the recently proposed MDIQKD with imperfect single-photon source such as the coherent states or the heralded states from the parametric down conversion. We point out that the existing result for secure QKD with source coding errors d…
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise which is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates are critical to these models. We use a Bayesian inference approach to identity posterior distributions of these parameters, such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM's quantum computing devices suggest that o…
Correctly characterizing state preparation and measurement (SPAM) processes is a necessary step towards building reliable quantum processing units (QPUs). In this work, we discuss the subtleties behind separately measuring SPAM errors. We propose a protocol that can separately estimate SPAM errors, in the case where quantum gates are ideal. In the case where the quantum gates are imperfect, we derive bounds on the estimated SPAM error rates, based on gate error measures which can be estimated independently of SPAM processes. Our method shows that the gauge ambiguity in characterizing SPAM oper…
What is the most efficient way to generate random numbers device-independently using a photon pair source based on spontaneous parametric down conversion (SPDC)? We consider this question by comparing two implementations of a detection-loophole-free Bell test. In particular, we study in detail a scenario where a heralded single photon source (HSPS) is used to herald path-entangled states, i.e. entanglement between two spatial modes sharing a single photon and where non-locality is revealed using photon counting preceded by small displacement operations. We start by giving a theoretical descrip…
A central challenge for many quantum technologies concerns the generation of large entangled states of individually addressable quantum memories. Here, we show that percolation theory allows the rapid production of arbitrarily large graph states by heralded photonic entanglement in a lattice of atomic memories. This approach can greatly reduce the time required to produce large cluster resource states for quantum information processing, including states required for universal one-way quantum computing. This reduction puts our architecture in an operational regime where demonstrated collection,…
Single-photon detection is an essential component in many experiments in quantum optics, but remains challenging in the microwave domain. We realize a quantum non-demolition detector for propagating microwave photons and characterize its performance using a single-photon source. To this aim we implement a cavity-assisted conditional phase gate between the incoming photon and a superconducting artificial atom. By reading out the state of this atom in single shot, we reach an internal photon detection fidelity of 71%, limited by the coherence properties of the qubit. By characterizing the cohere…
Spin-bath noise characterization, which is typically performed by multi-pulse control sequences, is essential for understanding most spin dynamics in the solid-state. Here, we theoretically propose a method for extracting the characteristic parameters of a noise source with a known spectrum, using a single modified Hahn-echo sequence. By varying the application time of the pulse, measuring the coherence curves of an addressable spin, and fitting the decay coefficients to a theoretical function derived by us, we extract parameters characterizing the physical nature of the noise. Assuming a Lore…
Reducing the noise below the shot-noise limit in sensing devices is one of the key promises of quantum technologies. Here, we study quantum plasmonic sensing based on an attenuated total reflection configuration with single photons as input. Our sensor is the Kretschmann configuration with a gold film, and a blood protein in an aqueous solution with different concentrations serves as an analyte. The estimation of the refractive index is performed using heralded single photons. We also determine the estimation error from a statistical analysis over a number of repetitions of identical and indep…
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability are employed to analyze the possibility of measuring together two general quantum observables, characterizing different degrees of compatibility between measurements. It is known that two jointly measurable observables are always coexistent, and that the converse holds for various classes of observables, including the case of observables with two outcomes. He…
The generation of entanglement between remote matter qubits has developed into a key capability for fundamental investigations as well as for emerging quantum technologies. In the single-photon, protocol entanglement is heralded by generation of qubit-photon entangled states and subsequent detection of a single photon behind a beam splitter. In this work we perform a detailed theoretical and experimental investigation of this protocol and its various sources of infidelity. We develop an extensive theoretical model and subsequently tailor it to our experimental setting, based on nitrogen-vacanc…
