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Self-Referenced Diagnosis of SPAD Dark-Count-Rate Switching for Quantum Communication Receivers

Yu Luo, Lina Pu, Yaroslav Koshka, Chun-Hung Liu, Junming Diao

arXiv:2610.37312v1cs.ET

TL;DR

SPAD dark-count steps can reflect intrinsic RTS or artifacts, and count-rate traces alone may not identify their cause. The paper uses state-resolved afterpulse yield with DCR, cross-channel, and timing checks; three modules showed ratios consistent with unity, while controlled artifacts produced distinct signatures.

  • Problem

    Step-like SPAD dark-count changes can arise from intrinsic RTS or external and readout effects, so the count-rate trace alone may not identify the switching mechanism.

    Source: §I · p. 1

  • Method

    The framework primarily compares low-to-high afterpulse-yield ratio R and supplements it with reproducibility, cross-channel, and event-timing checks.

    Source: §I · p. 1

  • Results

    Three modules showed DCR-state separations of 44.59%, 19.33%, and 2.77%, with R values 0.9996±0.0027, 1.0050±0.0023, and 1.0027±0.0043, all consistent with unity.

    Source: §I · p. 2

  • Takeaways & Limitations

    Intrinsic switching is supported when near-unity R is accompanied by abrupt, single-channel transitions, stable states, and no external-factor correlation.

    Source: C. Decision Criteria and Limitations · p. 7

    R ≃1 is not unique to intrinsic switching, and discrimination weakens as p approaches 1, making confidence intervals or hypothesis tests necessary.

    Source: C. Decision Criteria and Limitations · pp. 6–7

Abstract

from arXiv · show

Single-photon avalanche diodes (SPADs) are essential components of quantum communication receivers. In practical systems, some SPADs exhibit intrinsic step-like changes in dark-count rate (DCR), commonly referred to as random telegraph signal (RTS) noise. Similar RTS-like variations, however, can also arise from stray light, temperature-dependent threshold crossings, cable disturbances, electrical interference, and other readout artifacts. Distinguishing intrinsic RTS from these artifacts is important because they originate from different mechanisms and require different corrective actions. We present a self-referenced diagnostic that primarily uses the low-to-high afterpulse-yield ratio R, together with complementary checks based on DCR-state reproducibility, cross-channel behavior, and event timing. Four commercial SPAD modules were monitored in darkness for more than 920 h. Three exhibited intrinsic DCR switching of 44.59%, 19.33%, and 2.77%, with corresponding R values of $0.9996\pm0.0027$, $1.0050\pm0.0023$, and $1.0027\pm0.0043$, all consistent with unity. Controlled experiments reproduced temperature-related threshold crossings, light leakage, cable-contact artifacts, and artificial electrical injection. These artifacts produced distinct correlation and timing signatures: temperature-related threshold crossings gave intermediate pair-survival responses, cable disturbances and electrical injection generated sub-dead-time events, while light leakage produced simultaneous cross-channel switching and nonreproducible DCR levels. Combining R with orthogonal timing and DCR-based checks provides a practical self-referenced diagnostic framework for distinguishing intrinsic RTS from non-intrinsic artifacts using primarily time-tagged dark-count data.

I. INTRODUCTION

SPAD dark-count-rate steps can arise from intrinsic RTS or external and readout artifacts, so count-rate traces alone may not identify their cause. The paper proposes a self-referenced diagnosis using afterpulse yield and complementary checks, and reports preserved yield across intrinsic DCR states alongside distinct signatures from controlled artifacts.

I. INTRODUCTION

  • Because dark counts contribute to false detections and accidental coincidences, reliable DCR characterization matters especially in lossy quantum links where signal approaches detector background.Intrinsic RTS may call for detector recalibration or replacement, whereas optical leakage or readout faults require corrective action elsewhere in the receiver.Source: §I · p. 1
  • The diagnostic primarily compares low-to-high afterpulse-yield ratio R, then uses DCR-state reproducibility, cross-channel behavior, and event timing relative to detector dead time as complementary checks.The approach uses afterpulse correlations to test changes in avalanche population, counting loss, and count addition.Source: §I · pp. 1–2
  • The afterpulse-yield ratio can be extracted from time-tagged dark-count records already used for DCR monitoring, without dedicated measurements for initial diagnosis.The authors report more than 920 h of live acquisition across four commercial modules.Source: §I · p. 2
  • 44.59%, 19.33%, and 2.77% DCR-state separations in three modules had low-to-high afterpulse-yield ratios of 0.9996±0.0027, 1.0050±0.0023, and 1.0027±0.0043, respectively, all consistent with unity.The modules were monitored in darkness for more than 920 h across four commercial SPAD modules.Source: §I · p. 2
  • Controlled tests reproduced temperature-related threshold crossings, stray-light leakage, cable disturbances, and electrical injection, which produced distinct correlation, cross-channel, or event-timing signatures.Some mechanisms preserve afterpulse yield, so additional DCR- or timing-based checks may be needed.Source: §I · p. 2

II. RELATED WORK

Prior work characterizes SPAD RTS and afterpulsing, but does not generally compare correlated afterpulse yield between naturally occurring DCR states of the same detector. The paper introduces that comparison and describes the hardware, acquisition, and pair-counting procedure used to support it.

II. RELATED WORK

  • Earlier studies link discrete DCR states to defect-mediated mechanisms and characterize afterpulsing across devices, but generally do not compare correlated yield between natural high- and low-DCR states of one detector.The paper uses that state-conditioned yield as a diagnostic of count-rate transitions.Source: §II · pp. 2–3

A. System Hardware and Data Acquisition

  • Four SPAD modules connect to a four-channel TDC; two outputs pass through variable attenuators, while module and room temperatures are monitored with RTD sensors.Attenuators enable controlled amplitude-selective counting losses, and the setup also permits waveform measurements.Source: A. System Hardware and Data Acquisition · p. 3, Figure 1 · p. 3
  • The TDC records timestamped pulses in 60-second chunks, with event correlations calculated within each chunk and host timestamps used to align records with temperature measurements.No timing statistics span acquisition gaps between chunks.Source: A. System Hardware and Data Acquisition · p. 3

B. Afterpulse Identification

  • Afterpulsing is estimated from excess event pairs in the 60 ns–2.00 µs short-delay window above an accidental-pair baseline measured at 50–100 µs.For module #11971, the measured dead-time floor is approximately 50 ns; the short-delay window begins above that floor.Source: B. Afterpulse Identification · pp. 3–4

IV. RTS NOISE AND AFTERPULSING IN SPADS

Three of four modules showed resolved DCR states, while afterpulse yield remained consistent across those states despite variation over time and temperature. The state-to-state ratio R provides the self-reference for interpreting the switching.

A. Characteristics of RTS Noise

  • For #11971 and #11282, mean dwell times ranged from 2.66 to 7.22 h, with coefficients of variation from 0.95 to 1.06 and no significant deviation from exponential distributions.Successive dwell times were only weakly correlated, with no statistically significant dependence.Source: A. Characteristics of RTS Noise · p. 4
  • Three modules showed discrete DCR states near 177.38 ↔320.13 Hz, 296.17 ↔367.14 Hz, and 305.7 ↔314.4 Hz; #6802 showed no resolved state.The first two modules had irregular dwell times consistent with stochastic, approximately memoryless switching.Source: Figure 3 · p. 4, A. Characteristics of RTS Noise · p. 4
  • The abrupt transitions did not consistently coincide with smooth temperature cycles or occur simultaneously across modules, so switching is identified by within-device discrete changes rather than absolute DCR.Absolute DCR differed substantially among modules of the same commercial series.Source: A. Characteristics of RTS Noise · p. 4
  • For #11971, the pooled 95% upper limit on transition duration was τ <21 µs; for #11282 it was τ < 0.17 ms.The bounds are limited primarily by stochastic dark-count statistics, so abruptness does not establish zero physical transition duration or exclude faster dynamics.Source: A. Characteristics of RTS Noise · p. 4

B. Afterpulsing Across Rate States

  • Absolute afterpulse yield varied among modules and drifted by 2.0%–7.5% over 44 daily measurements, but R remained stable as common-mode yield variations largely canceled.The low-to-high ratio quantifies preservation of afterpulse yield between resolved DCR states.Source: B. Afterpulsing Across Rate States · p. 5
  • R = 0.9996 ± 0.0027, 1.0050 ± 0.0023, and 1.0027 ± 0.0043 for #11971, #11282, and #6804, respectively, despite DCR changes of 44.59%, 19.33%, and 2.77%.All three ratios are statistically consistent with unity over 44 days.Source: B. Afterpulsing Across Rate States · p. 5

V. SELF-REFERENCED DIAGNOSTIC METHOD

The diagnostic compares the low-to-high afterpulse-yield ratio R with predictions for avalanche-population change, independent counting loss, and uncorrelated count addition. R summarizes correlated events per recorded detection across the two DCR states.

V. SELF-REFERENCED DIAGNOSTIC METHOD

  • The section develops afterpulse-yield ratio tests for population change, independent loss, and uncorrelated addition, then introduces a normalized pair-survival statistic for correlated loss.Auxiliary checks and diagnostic limitations are also discussed.Source: §V · p. 5

A. Rate- and Yield-Ratio Tests

  • R compares correlated events per recorded detection across the low- and high-DCR states, not the total afterpulses generated.Because the yields use the same detector and timing windows, their ratio suppresses slow changes common to both states.Source: A. Rate- and Yield-Ratio Tests · p. 5
  • For avalanche-population change, detection and correlated-pair counts scale together, predicting R ≃1; independent loss predicts R ≃p.Uncorrelated count addition predicts R ≃1/p.Source: A. Rate- and Yield-Ratio Tests · p. 5
  • R ≃1, when R = p and R = 1/p are rejected, excludes independent-loss and uncorrelated-addition models but does not alone establish the switching mechanism.Correlated pair loss and added photon-induced avalanches can also preserve afterpulse yield.Source: A. Rate- and Yield-Ratio Tests · p. 5

B. Normalized Pair-Survival Statistic

The normalized pair-survival statistic ρs is calculated from the measured ratios R and p under an equal-marginal pure-loss model. Its interpretation as physical survival correlation depends on that model's assumptions.

B. Normalized Pair-Survival Statistic

  • ρs = (R−p)/(1−p) gives the survival correlation inferred from measured R and p under the equal-marginal pure-loss model.The paper calls ρs the normalized pair-survival statistic.Source: B. Normalized Pair-Survival Statistic · p. 6
  • Independent survival gives ρs = 0, partially correlated survival gives 0 < ρs < 1, and identical survival outcomes give ρs = 1.Equal marginal survival probabilities alone do not imply identical outcomes.Source: B. Normalized Pair-Survival Statistic · p. 6
  • ρs equals physical survival correlation only under equal-marginal pure loss; outside that model, it is a normalized pair-survival diagnostic, not necessarily a Pearson correlation.With unequal marginal survival probabilities, recovering physical correlation requires separate estimates of px and py.Source: B. Normalized Pair-Survival Statistic · p. 6
  • For genuine avalanche-generation changes, no unchanged high-state pulse stream is being filtered, so ρs remains a diagnostic comparison with counting loss rather than a physical survival correlation.Source: B. Normalized Pair-Survival Statistic · p. 6

C. Decision Criteria and Limitations

The decision procedure combines R and p comparisons with state, environmental, channel, and timing checks, using ρs when correlated counting loss remains plausible. Its discrimination weakens as p approaches 1.

C. Decision Criteria and Limitations

  • The diagnostic identifies recurrent abrupt DCR states, checks temperature and other channels, compares R with 1, p, and 1/p, then uses ρs for plausible correlated loss.Uncertainty estimates resample complete dwells or measurement blocks, and correlated-loss tests are compared with controlled threshold-loss measurements.Source: C. Decision Criteria and Limitations · p. 6, Figure 4 · p. 6
  • Within equal-marginal pure loss, ρs ranges from 0 for independent survival to 1 for identical survival outcomes; outside pure loss, it is not a physical Pearson correlation.Source: C. Decision Criteria and Limitations · p. 6
  • R ≃1 alone cannot establish detector-local switching because perfectly correlated counting loss and stray-light avalanches can also preserve afterpulse yield.Source: C. Decision Criteria and Limitations · p. 6
  • Detector-local switching is supported when R rejects loss and addition predictions and transitions are abrupt, random, single-channel, state-stable, and uncorrelated with external factors or pulse-height changes.Together, these observations reject the tested independent-loss, uncorrelated-addition, common-mode, thermal, and pulse-amplitude mechanisms.Source: C. Decision Criteria and Limitations · p. 7
  • As p →1, the predictions R = 1, R = p, and R = 1/p converge, so discrimination depends on DCR separation and measurement uncertainty.The paper recommends confidence intervals or hypothesis tests rather than fixed thresholds.Source: C. Decision Criteria and Limitations · p. 7

VI. TEMPERATURE-RELATED ARTIFACTS

Temperature-dependent pulse amplitudes can create RTS-like recorded-rate changes when the TDC threshold lies near the pulse top. Their intermediate afterpulse response distinguishes this artifact from intrinsic RTS, which preserves afterpulse yield across DCR states.

VI. TEMPERATURE-RELATED ARTIFACTS

  • Restricting analysis to the intrinsic high-DCR state showed that pulse-top thresholds alone can produce RTS-like rate changes.The experiment stepped the TDC threshold cyclically while the detector remained sealed in darkness.Source: §VI · p. 7
  • At the normal operating threshold, the count rate remained near 324 Hz, varying by less than 0.4% throughout the temperature cycles, while rates near the pulse top showed pronounced temperature dependence.At 2.269 V, the rate increased by 8.2% and 8.0% for cooling steps of 3.4 and 3.6 K, respectively, and decreased by 7.5% for a warming step of 3.0 K.Source: §VI · pp. 7–8
  • Temperature shifts primary and afterpulse peak amplitudes by about −2.6 mV/K while changing pulse-to-pulse width only weakly.The normal operating threshold lies below the pulse top, but a threshold near the amplitude flank can convert these shifts into count changes.Source: §VI · p. 8, Figure 7 · p. 8
  • Primary and afterpulse amplitudes are correlated but not identical, so threshold losses are neither independent nor perfectly correlated.The afterpulse–primary amplitude difference reaches 11.8 mV at a delay of 326 ns before decreasing.Source: §VI · p. 8, Figure 8 · p. 8
  • At 2.269 V, R = 0.959 ± 0.013 (p = 0.901), and at 2.309 V, R = 0.842 ± 0.036 (p = 0.690), indicating intermediate pair survival.These responses fall between independent loss (R = p) and fully correlated loss (R = 1).Source: §VI · p. 8, Table I · p. 8
  • Intrinsic RTS instead gives R = 0.9996±0.0027 despite p = 0.554, separating it from temperature-related threshold crossings.The intrinsic transition has ρs = 0.999 ± 0.006, whereas the threshold-crossing cases have intermediate ρs values.Source: §VI · p. 8, Table I · p. 8

VII. ENVIRONMENT-INDUCED ARTIFACTS

Environmental changes, including ambient-light leakage and cable-related loss, can produce RTS-like DCR steps. Because these artifacts can resemble intrinsic RTS and R alone may not distinguish them, the section combines self-referenced metrics with features in the DCR record.

VII. ENVIRONMENT-INDUCED ARTIFACTS

  • Ambient-light leakage and cable-related loss are examined as environmental causes of RTS-like DCR steps.These artifacts can reproduce features of intrinsic RTS.Source: §VII · p. 8
  • The artifacts cannot always be identified from the afterpulse-yield ratio R alone.The section distinguishes them using characteristic features observed directly in the DCR record.Source: §VII · pp. 8–9
  • The diagnostic combines self-referenced metrics with DCR-record features to distinguish environmental artifacts from intrinsic RTS.The section focuses on ambient-light leakage and cable-related loss.Source: §VII · pp. 8–9

A. RTS-Like Artifacts Caused by Light Leakage

Light leakage can create abrupt, bimodal DCR changes that resemble intrinsic RTS, but simultaneous changes across channels and nonreproducible rate levels identify the external optical source. The near-unity afterpulse signature and sharp transitions alone do not distinguish leakage from intrinsic switching.

A. RTS-Like Artifacts Caused by Light Leakage

  • All four modules switched simultaneously during light exposure, with mean induced steps of approximately 543 Hz for #11282, 61 Hz for #6804, 35 Hz for #11971, and 13 Hz for #6802.On a single channel, these abrupt two-level changes can resemble intrinsic RTS.Source: A. RTS-Like Artifacts Caused by Light… · pp. 9–10, Figure 9 · p. 9
  • Light-leak transitions had no resolvable finite ramp, with a pooled 95% upper limit of τ < 0.42 ms, so sharpness alone cannot identify intrinsic RTS.Source: A. RTS-Like Artifacts Caused by Light… · p. 9
  • For #11282, dark levels varied from 359.5 to 399.9 Hz and illuminated levels from 867.8 to 956.2 Hz, unlike reproducible intrinsic RTS levels.The corresponding light-induced step varied from approximately 508 to 566 Hz.Source: A. RTS-Like Artifacts Caused by Light… · p. 9
  • Daylight mainly shifts both dark and illuminated baselines, while the rate difference across each switching edge isolates the ceiling-lamp contribution.For example, during 09:24–10:24, the illuminated and dark levels rose by 24.3 and 21.7 Hz, while the switch-edge steps differed by 2.6 Hz.Source: A. RTS-Like Artifacts Caused by Light… · p. 9
  • The first lamp-induced step averaged 512.8±5.6 Hz, 7.3% below the later daytime average of 553.1±3.3 Hz, consistent with warmer fixture conditions.The first period began at a room temperature of approximately 25.1 °C, versus 21.8–22.1 °C during later switching events.Source: A. RTS-Like Artifacts Caused by Light… · p. 9, Figure 10 · p. 9
  • For #11282, light-induced states gave R = 1.015 ± 0.012 and ρs = 1.03 ± 0.02, a near-unity signature also seen in intrinsic RTS.Cross-channel coincidence and externally determined dwell intervals, rather than afterpulse statistics alone, identify leakage.Source: A. RTS-Like Artifacts Caused by Light… · p. 10

B. Cable-Induced Counting Artifacts

Cable contact can produce irregular count bursts and dropouts, rather than the stable levels of intrinsic RTS. Sub-dead-time events and abnormal afterpulse statistics further identify this as a readout artifact.

B. Cable-Induced Counting Artifacts

  • Cable twisting produced irregular bursts reaching several kilohertz and signal dropouts around a 300 Hz baseline, unlike stable intrinsic RTS levels.The reference detector remained near its approximately 370 Hz baseline without comparable excursions.Source: B. Cable-Induced Counting Artifacts · p. 10
  • Cable twisting reduced the minimum event interval to 4 ns, with approximately 1.90% of intervals below the 48 ns dead-time floor.Such sub-dead-time events are attributed to electrical multi-triggering or contact-induced ringing, not genuine SPAD avalanches.Source: B. Cable-Induced Counting Artifacts · p. 10, Figure 11 · p. 10
  • During cable twisting, R = 1.283 with p = 0.822 and ρs = 2.59, outside the pure-loss range 0 ≤ρs ≤1.Contact-induced multi-triggering adds correlated counts within the afterpulse analysis window.Source: B. Cable-Induced Counting Artifacts · p. 10

VIII. READOUT-DEPENDENT ARTIFACTS

Matched electrical injection can reproduce the detector’s afterpulse yield, but sub-dead-time events expose its non-intrinsic origin. Uncorrelated downstream counts instead raise the afterpulse-yield ratio and may violate the detector’s dead-time structure.

1) Artificial Injection:

  • Matching the detector’s DCR and primary–afterpulse statistics can leave R ≃1 inconclusive because injected pulses bypass the avalanche and recovery process.Mimicking intrinsic RTS would also require reproducing the detector’s physical recovery constraint.Source: 1) Artificial Injection · pp. 10–11
  • 40 injected events fell within 28–48 ns, below the detector’s 48 ns minimum, despite R = 1.002 ± 0.020 and ρs ≃1.The injection therefore matched the afterpulse yield but not the detector’s dead-time behavior.Source: 1) Artificial Injection · p. 11, Figure 12 · p. 11

2) Interference-Induced Random Counting Addition:

  • Uncorrelated downstream counts increase singles without corresponding primary–afterpulse pairs, giving R = 1/p; a 10% rate increase predicts R ≈1.10 and ρs ≈2.1.This differs from intrinsic RTS, for which R ≃1.Source: 2) Interference-Induced Random… · p. 11
  • R > 1, ρs > 1, and sub-dead-time events together indicate interference-induced counting, although bursts or correlated interference can break the ideal R = 1/p relation.Downstream electronic counts are not inherently constrained by SPAD recovery time.Source: 2) Interference-Induced Random… · p. 11

B. Electronics-Induced Counting Loss

The diagnostic combines afterpulse-yield behavior with timing and reproducibility because readout artifacts can mimic DCR switching. Independent or partially coupled counting loss often gives R < 1, but common-mode loss and history-dependent processes can make R and ρs alone inconclusive.

B. Electronics-Induced Counting Loss

  • Pulse-width discrimination is not simple independent thinning: rejected avalanches still affect detector state, and the pair-survival probability depends on the primary–afterpulse delay.Here ρs is only a normalized diagnostic statistic, and published data are insufficient to determine R.Source: B. Electronics-Induced Counting Loss · p. 12
  • Selective counting loss gives R < 1 under independent or partially correlated survival, but nearly common loss can also produce R ≃1.History- and delay-dependent pulse-width discrimination may not be diagnosed by R and ρs alone; time-tagged DCR behavior is also needed.Source: B. Electronics-Induced Counting Loss · p. 12

IX. CONCLUSION

  • Intrinsic RTS in the tested receivers showed reproducible detector-specific rate states, approximately memoryless dwell times, and abrupt switching without a resolvable ramp.The ratio of afterpulse yield between resolved states remained stable despite variation in absolute yield across devices, time, and temperature.Source: §IX · p. 12
  • Temperature-induced threshold crossings gave R = 0.959±0.013 at 2.269 V and R = 0.842±0.036 at 2.309 V, unlike intrinsic RTS with R = 0.9996 ± 0.0027.Cable-contact disturbances also produced short-delay events below the SPAD dead-time floor.Source: §IX · p. 12
  • Light leakage can preserve afterpulse yield, while matched electrical injection can give R = 1.002 ± 0.020; timing and DCR reproducibility therefore complement R and ρs.The injection still produced events below the dead-time floor, whereas light-leakage behavior varied with temperature and source thermal state.Source: §IX · p. 12
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