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Harnessing Data Augmentation to Quantify Uncertainty in the Early Estimation of Single-Photon Source Quality

David Jacob Kedziora, Anna Musiał, Wojciech Rudno-Rudziński, Bogdan Gabrys

TL;DR

The paper addresses the challenge of rapidly estimating single-photon source quality while rigorously accounting for counting-statistics uncertainty. It introduces a Poisson-based, cosh-represented model of two-photon coincidence histograms and demonstrates data augmentation via Poisson-sampled synthetic histograms to quantify sampling-based error in the SPS quality metric $g^{(2)}(0)$. Across eight InGaAs/GaAs quantum-dot datasets, it shows irreducible uncertainty from Poisson variability, finds no clear advantage of Poisson-likelihood fitting over least-squares, and highlights expanding averages as a potential early estimator. The work provides a practical methodology and open resources for robust uncertainty quantification in SPS characterization, guiding when faster estimates are trustworthy and emphasizing the need to account for stochastic counting statistics and background contributions in claims of state-of-the-art performance.

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.

Harnessing Data Augmentation to Quantify Uncertainty in the Early Estimation of Single-Photon Source Quality

TL;DR

The paper addresses the challenge of rapidly estimating single-photon source quality while rigorously accounting for counting-statistics uncertainty. It introduces a Poisson-based, cosh-represented model of two-photon coincidence histograms and demonstrates data augmentation via Poisson-sampled synthetic histograms to quantify sampling-based error in the SPS quality metric . Across eight InGaAs/GaAs quantum-dot datasets, it shows irreducible uncertainty from Poisson variability, finds no clear advantage of Poisson-likelihood fitting over least-squares, and highlights expanding averages as a potential early estimator. The work provides a practical methodology and open resources for robust uncertainty quantification in SPS characterization, guiding when faster estimates are trustworthy and emphasizing the need to account for stochastic counting statistics and background contributions in claims of state-of-the-art performance.

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.
Paper Structure (9 sections, 7 equations, 10 figures, 5 tables)

This paper contains 9 sections, 7 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Methodology
  4. The Datasets
  5. The Fitting Procedure
  6. Data Augmentation
  7. Results
  8. Discussion
  9. Conclusion

Figures (10)

  • Figure 1: The total number of two-photon events ($0\leq \tau_r\lesssim 5.0e-7$) detected within every $10$ s snapshot for the duration of the 4uW experiment.
  • Figure 2: Histogram of two-photon events detected during the entire 4uW experiment, as well as during the first $10$ s snapshot. The count axis is logarithmic. (a) A view of the entire $\tau_r$ domain. (b) A closeup around the MPE peak.
  • Figure 3: Closeups of example histograms Poisson-sampled from the best least-squares fit for the 2p5uW experiment. Displays the original best fit from which the histogram is sampled as well as a new fit, both scaled for the appropriate duration $t$. Histogram contains approximately: (a) 1000 events, (b) 51534 events, i.e. the original size of the full dataset that dictated the best fit, and (c) 1000000 events.
  • Figure 4: Comparison of least-squares fitted parameter $g$ between the 'ground-truth' best fit for the 2p5uW experiment and fits applied to subsequent Poisson-sampled histograms. There are 250 histograms generated for each of the following approximate numbers of total events: 1.0e3, 1.0e4, 1.0e5, and 1.0e6. There are also 250 generated for approximately the same number of events as used for the best fit, i.e. 51534 for 2p5uW.
  • Figure 5: Comparison of least-squares fitted parameter $g$, per dataset, between the 'ground-truth' best fit and fits applied to 250 subsequent Poisson-sampled histograms of approximate size 1.0e5.
  • ...and 5 more figures