Abstract Novel methods for rapidly estimating single-photon source (SPS) quality have been promoted in recent literature to address the expensive and time-consuming nature of experimental validation via intensity interferometry. However, the frequent lack of uncertainty discussions and reproducible details raises concerns about their reliability. This study investigates the use of data augmentation, a machine learning technique, to supplement experimental data with bootstrapped samples and quantify the uncertainty of such estimates. Eight datasets obtained from measurements involving a single InGaAs/GaAs epitaxial quantum dot serve as a proof-of-principle example. Analysis of one of the SPS quality metrics derived from efficient histogram fitting of the synthetic samples, i.e. the probability of multi-photon emission events, reveals significant uncertainty contributed by stochastic variability in the Poisson processes that describe detection rates. Ignoring this source of error risks severe overconfidence in both early quality estimates and claims for state-of-the-art SPS devices. Additionally, this study finds that standard least-squares fitting is comparable to using a Poisson likelihood, and expanding averages show some promise for early estimation. Also, reducing background counts improves fitting accuracy but does not address the Poisson-process variability. Ultimately, data augmentation demonstrates its value in supplementing physical experiments; its benefit here is to emphasise the need for a cautious assessment of SPS quality.
Abstract Novel methods for rapidly estimating single-photon source (SPS) quality have been promoted in recent literature to address the expensive and time-consuming nature of experimental validation via intensity interferometry. However, the frequent lack of uncertainty discussions and reproducible details raises concerns about their reliability. This study investigates the use of data augmentation, a machine learning technique, to supplement experimental data with bootstrapped samples and quantify the uncertainty of such estimates. Eight datasets obtained from measurements involving a single InGaAs/GaAs epitaxial quantum dot serve as a proof-of-principle example. Analysis of one of the SPS quality metrics derived from efficient histogram fitting of the synthetic samples, i.e. the probability of multi-photon emission events, reveals significant uncertainty contributed by stochastic variability in the Poisson processes that describe detection rates. Ignoring this source of error risks severe overconfidence in both early quality estimates and claims for state-of-the-art SPS devices. Additionally, this study finds that standard least-squares fitting is comparable to using a Poisson likelihood, and expanding averages show some promise for early estimation. Also, reducing background counts improves fitting accuracy but does not address the Poisson-process variability. Ultimately, data augmentation demonstrates its value in supplementing physical experiments; its benefit here is to emphasise the need for a cautious assessment of SPS quality.
Abstract The use of single-photon sources (SPSs) is central to numerous systems and devices proposed amidst a modern surge in quantum technology. However, manufacturing schemes remain imperfect, and single-photon emission purity must often be experimentally verified via interferometry. Such a process is typically slow and costly, which has motivated growing research into whether SPS quality can be more rapidly inferred from incomplete emission statistics. Hence, this study is a sequel to previous work that demonstrated significant uncertainty in the standard method of quality estimation, i.e. the least-squares fitting of a physically motivated function, and asks: can machine learning (ML) do better? The study leverages eight datasets obtained from measurements involving an exemplary quantum emitter, i.e. a single InGaAs/GaAs epitaxial quantum dot; these eight contexts predominantly vary in the intensity of the exciting laser. Specifically, via a form of ‘transfer learning’, five ML models, three linear and two ensemble-based, are trained on data from seven of the contexts and tested on the eighth. Validation metrics quickly reveal that even a linear regressor can outperform standard fitting when it is tested on the same contexts it was trained on, but the success of transfer learning is less assured, even though statistical analysis, made possible by data augmentation, suggests its superiority as an early estimator. Accordingly, the study concludes by discussing future strategies for grappling with the problem of SPS context dissimilarity, e.g. feature engineering and model adaptation.
Second-order photon correlation measurements [${g}^{(2)}(\ensuremath{\tau})$ functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations -- such as quantum dots -- by evaluating the value of ${g}^{(2)}(\ensuremath{\tau}=0)$. Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free ${g}^{(2)}(\ensuremath{\tau})$ functions from noise-dominated, few-shot inputs. The model is trained with simulated ${g}^{(2)}(\ensuremath{\tau})$ functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of ${g}^{(2)}(\ensuremath{\tau}=0)$ that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot ${g}^{(2)}(\ensuremath{\tau})$ functions (\ensuremath{\sim}100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free ${g}^{(2)}(\ensuremath{\tau})$ functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. This work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.
Single-photon sources are used in numerous quantum technologies, from sensing and imaging to communication, making the accurate modeling of their emissions essential. In this work, we propose a statistical framework for describing single-photon emission processes and implement estimators for the exponential distribution to quantify this phenomenon. Our approach provides a reliable method for estimating the radiative decay time, represented by the inverse rate parameter, which is crucial in quantum optics applications. We explore several statistical estimators, including maximum likelihood estimation, minimum-variance unbiased estimator, and best linear unbiased estimator. To validate our theoretical methods, we test the proposed estimators on experimental data, demonstrating their applicability in real-world settings. We also evaluate the performance of these estimators when dealing with censored data, a frequent limitation in photon emission experiments. The analysis allows us to track the performance of the proposed estimators as the amount of available data decreases, providing insights into their reliability for modeling single-photon emission events under limited resources.
Estimating the quality of a single-photon source is crucial for its use in quantum technologies. The standard test for semiconductor sources is a value of the second-order correlation function of the emitted field below 1/2 at zero time delay. This criterion alone provides no information regarding the amplitude of the single-photon contribution for general quantum states. Addressing this question requires the knowledge of additional observables. We derive an effective second-order correlation function, strongly connected to the Mandel-Q parameter and given in terms of both the second-order correlation and the average photon number, that provides a lower bound on the single-to-multiphoton projection ratio. Using both observables individually allows for lower and upper bounds for the single-photon projection. Comparing the tightness of our bounds with those in the literature, we find that relative bounds may be better described using the average photon number, while absolute bounds for low excitation states are tighter using the vacuum projection. Our results show that estimating the quality of a single-photon source based on additional information is very much dependent on what aspect of the quantum state of light one is interested in.
The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér–Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.
Historically non-classical sources of single photons have been used to test quantum mechanics and to develop the field of quantum optics. Nowadays the single photon source has become a critical device for quantum communications and optical quantum information processing [Knill, et al., 2001]. A single photon source emits one photon at a time, and its quality can be evaluated by three parameters: quantum efficiency, multi-photon probability, and photon distinguishability. Among the different types single photon sources, InGaAs/GaAs quantum dots (QDs) are a promising solid state candidate showing high quantum efficiency, no bleaching effect, long-term stability, capable of high repetition rate, and compatible with standard semiconductor processing techniques. Furthermore, QDs can be embedded in micro-cavities or photonic crystal nano-cavities by in situ growth, and thus cavity quantum electrodynamics (CQED) can be exploited to improve the performance of QD-based single photon sources in all aspects mentioned above [Santori, et al., 2002].