Shot Noise Calibration (SNC)

• SNC is a calibration technique that uses the predictable quantum (or Poissonian) noise of discrete charge or photon transport as an absolute reference.
• It bridges microscopic noise processes and macroscopic observables, enabling precise measurement and normalization in electronic, optical, and quantum systems.
• Effective SNC implementation requires rigorous control of reference planes and modeling of spectral structures to address system nonlinearities and ensure traceable calibration.

Shot Noise Calibration (SNC) denotes calibration procedures that use the predictable noise generated by discrete charge or photon transport as a metrological reference. In the literature, SNC appears in closely related forms: as an absolute calibration of current or microwave noise through the law $S_I = 2 q \bar{I}$; as a normalization of homodyne or heterodyne measurements in shot-noise units (SNU); and as a calibration of the signal-dependent term in heteroscedastic noise models such as $K_\text{shot}^2 = g/\langle I\rangle$ or $\sigma^2(x) = a x + b$ (Chen, 2018, Zhang et al., 2019, Ricard et al., 9 Sep 2025, Liu et al., 18 Jun 2025, Bhatt, 17 Dec 2025). Across these settings, the common premise is that once the reference plane, bandwidth, and stochastic model are fixed, the fluctuation level associated with discrete quanta can serve as an absolute or quasi-absolute calibration observable.

1. Physical basis and spectral structure

In the electronic transport sense, shot noise is derived from a current modeled as a train of Dirac pulses,

$I(t) = \sum_i q\,\delta(t-t_i),$

with independent Poissonian arrivals at rate $\lambda=\bar I/q$. Under stationarity, ergodicity, and ideal detection bandwidth, the one-sided current power spectral density is

$S_o(f)=2q\bar I.$

This is the canonical SNC relation: the noise spectral density is proportional to the carrier charge and to the DC current, and is white over the relevant band (Chen, 2018).

The same discreteness of charge produces the signal traditionally called Schottky noise in a circular accelerator, but the spectral organization is different. For a coasting beam with revolution period $T$ and frequency $f_r=1/T$, the pickup current is

$$I(t)=\sum_{i=1}^N\sum_{n=-\infty}^{\infty}q\,\delta(t-t_i-nT),$$

and the corresponding spectrum is a line comb,

$$S_c(f)\simeq 2q\bar I f_r\sum_{k=1}^{\infty}\delta(f-kf_r),$$

rather than a flat continuum. The integrated power in any interval of width $K_\text{shot}^2 = g/\langle I\rangle$0 around a harmonic matches the shot-noise value, but the spectral pattern remains inherently distinct. Accordingly, the paper concludes that Schottky noise is “not the same as, but a special realization of, the shot noise” (Chen, 2018).

This distinction is central for SNC. In linear electronic transport, calibration uses a white PSD over a measurement bandwidth $K_\text{shot}^2 = g/\langle I\rangle$1. In a storage ring, calibration uses the integrated power of narrow revolution harmonics or Schottky bands. Treating the latter as a broadband white floor is a categorical error.

2. Calibrated observables, reference units, and normalization

In current metrology and low-noise electronics, SNC exploits the direct relation between microscopic current fluctuations and macroscopic observables. If the current noise passes through an impedance $K_\text{shot}^2 = g/\langle I\rangle$2, then

$K_\text{shot}^2 = g/\langle I\rangle$3

and over a flat band of width $K_\text{shot}^2 = g/\langle I\rangle$4,

$K_\text{shot}^2 = g/\langle I\rangle$5

when $K_\text{shot}^2 = g/\langle I\rangle$6. This permits calibration of amplifier gain, analyzer power scale, impedance response, or current source amplitude from a noise law involving only $K_\text{shot}^2 = g/\langle I\rangle$7, $K_\text{shot}^2 = g/\langle I\rangle$8, and the transfer function (Chen, 2018).

In integrated coherent receivers, SNC is defined differently but plays an analogous role. The paper “Quantum coherent transceivers toward Holevo-limited communications” defines shot noise clearance as the ratio between the total noise power at maximum local-oscillator power and the electronic noise power with no local oscillator, with a knee power $K_\text{shot}^2 = g/\langle I\rangle$9 at which shot noise equals electronics and an effective efficiency contribution

$\sigma^2(x) = a x + b$0

In that setting SNC quantifies whether the receiver noise floor is dominated by optical shot noise rather than electronics or technical LO noise (Gurses et al., 8 Apr 2026).

In continuous-variable quantum key distribution, the calibration target is the shot-noise unit. The shot-noise unit is the variance of the vacuum noise at the input of an ideal homodyne detector, expressed in units where the vacuum quadrature variance is $\sigma^2(x) = a x + b$1. All measured quadratures, modulation variances, and excess-noise quantities are normalized to this reference. Because excess noise and key-rate formulas are expressed in SNU, any bias in the SNU estimate directly rescales the inferred covariance matrix and the security analysis (Zhang et al., 2019).

A broader inference follows from these uses. SNC is less a single instrument-specific routine than a normalization strategy in which a predictable quantum or Poissonian fluctuation level defines the scale of subsequent measurements.

3. Calibration architectures, reference planes, and absolute traceability

Absolute SNC depends not only on the noise law but also on where that law is referred. In cryogenic microwave experiments, the relevant problem is to determine absolute noise figures at the reference planes of the device under test. The paper “Device-Agnostic Microwave Noise Metrology for Nonlinear Cryogenic Quantum Devices” treats shot-noise calibration as one possible absolute reference and contrasts it with an in situ thermal-noise protocol based on Planck spectroscopy of a Variable Temperature Stage combined with cryogenic Short-Open-Load-Reciprocal calibration. Its central architectural result is that calibration should be separated from the DUT by substitution rather than performed in series through the DUT when the DUT is nonlinear or multimode (Celotto et al., 27 May 2026).

That separation is metrologically consequential. In a serial configuration, a controllable noise source placed at the DUT input requires a model of how noise propagates through the DUT. For nonlinear multimode devices, the paper shows that the true calibration law acquires a nonlinear, monotonic, convex correction $\sigma^2(x) = a x + b$2; fitting the resulting curve with a linear model overestimates the gain and underestimates the effective noise offset. The substitution configuration removes the DUT from the calibration path, allowing $\sigma^2(x) = a x + b$3 and $\sigma^2(x) = a x + b$4 to be referred to the same cryogenic planes as the SOLR-calibrated scattering parameters and then reused for DUT measurements without assuming a simplified internal noise model (Celotto et al., 27 May 2026).

The same paper explicitly notes that this architecture is compatible with shot-noise references. A shot-noise tunnel junction could replace the thermal source, with the predictable law $\sigma^2(x) = a x + b$5 supplying the calibration reference while the same cryogenic switch network defines the reference planes and de-embeds the network. This suggests that, in modern microwave metrology, SNC is increasingly understood as one member of a broader class of predictable-noise-source calibrations whose rigor depends on reference-plane control and on explicit separation of calibration from DUT dynamics.

4. Imaging, spectroscopy, and heteroscedastic SNC

In optical imaging and spectroscopy, SNC often takes the form of calibrating a signal-dependent variance model rather than an absolute noise temperature or current PSD. In speckle contrast optical spectroscopy, the measured contrast is decomposed as

$\sigma^2(x) = a x + b$6

with

$\sigma^2(x) = a x + b$7

Miscalibration of $\sigma^2(x) = a x + b$8 or $\sigma^2(x) = a x + b$9 leaves residual terms proportional to $I(t) = \sum_i q\,\delta(t-t_i),$0 and $I(t) = \sum_i q\,\delta(t-t_i),$1, whose temporal structure can mimic cerebral blood-volume waveforms because $I(t) = \sum_i q\,\delta(t-t_i),$2 itself is modulated by absorption. The proposed refinement minimizes the squared Volume-Flow Similarity Index, $I(t) = \sum_i q\,\delta(t-t_i),$3, by optimizing $I(t) = \sum_i q\,\delta(t-t_i),$4 and $I(t) = \sum_i q\,\delta(t-t_i),$5 with Adam. On 10 human subjects, this lowered the signal threshold for reliable CBF signal from 97 to 26 electrons per pixel for a $I(t) = \sum_i q\,\delta(t-t_i),$6 pixels SCOS system (Liu et al., 18 Jun 2025).

In photon-counting EMCCDs, SNC is embodied in the forward and inverse statistical model linking photon flux, thresholded counts, and corrected signal estimate. The pre-gain electron number is Poisson with mean

$I(t) = \sum_i q\,\delta(t-t_i),$7

while post-threshold counts are Bernoulli or binomial through the exceedance probability $I(t) = \sum_i q\,\delta(t-t_i),$8. Photometric corrections invert the nonlinear count-loss map and recover an estimator $I(t) = \sum_i q\,\delta(t-t_i),$9 of the true electron rate. In the Roman coronagraph simulation studied in the paper, uncorrected photon counting recovered a signal of $\lambda=\bar I/q$0 e$\lambda=\bar I/q$1 against a true $\lambda=\bar I/q$2 e$\lambda=\bar I/q$3, whereas the corrected estimator recovered $\lambda=\bar I/q$4 e$\lambda=\bar I/q$5; the theoretical corrected SNR, $\lambda=\bar I/q$6, matched the simulated mean SNR $\lambda=\bar I/q$7 (Ludwick, 2022).

The SNIC work generalizes the same logic to digital image synthesis. It adopts the Poisson–Gaussian model

$\lambda=\bar I/q$8

estimates $\lambda=\bar I/q$9 and $S_o(f)=2q\bar I.$0 per sensor, per ISO, and per CFA channel by photon-transfer analysis on flat fields, uses Huber regression for outlier rejection followed by least squares for the final fit, and supplements the model with dark frames when this improves realism. The resulting dataset contains over 6000 noisy images in RAW and TIFF formats, and the synthesized images outperform manufacturer-provided DNG noise models in LPIPS and in tests with a state-of-the-art denoiser (Bhatt, 17 Dec 2025).

These examples support a useful synthesis. In imaging, SNC is frequently a calibration of the linear coefficient governing signal-dependent variance, together with the conditions under which that coefficient remains stable or must be adapted.

5. Shot-noise units, receiver models, and CV-QKD security

In CV-QKD, SNC is security-critical because the shot-noise unit sets the normalization scale of all estimated channel parameters. The traditional two-time evaluation measures $S_o(f)=2q\bar I.$1 with both signal and LO blocked, then $S_o(f)=2q\bar I.$2 with LO on and signal blocked, and defines

$S_o(f)=2q\bar I.$3

The paper argues that this model omits additive LO-related terms such as relative-intensity noise, so in practice $S_o(f)=2q\bar I.$4. The resulting normalization no longer matches the entanglement-based detector model, and even a $S_o(f)=2q\bar I.$5 SNU deviation can significantly reduce the key rate and drive it to zero beyond about $S_o(f)=2q\bar I.$6 km in the simulation shown (Zhang et al., 2019).

The proposed remedy is a one-time calibration based on a trusted detector model. Instead of subtracting electronic noise, the joint shot-noise unit is defined as

$S_o(f)=2q\bar I.$7

or, in the extended model,

$S_o(f)=2q\bar I.$8

After normalization by $S_o(f)=2q\bar I.$9, the practical prepare-and-measure output becomes equivalent to the output of an entanglement-based detector model with beamsplitter transmissivities $T$0 and $T$1. The method reduces hardware complexity to one optical switch, reduces statistical fluctuation relative to the two-step procedure, and in a proof-of-principle experiment produced $T$2 kbps asymptotic and $T$3 kbps finite-size key rates at $T$4 km (Zhang et al., 2019).

A later development formalizes SNC under noise dynamics. “Receiver Noise Calibration in CV-QKD accounting for Noise Dynamics” introduces an operational framework based on Wide-Sense Stationarity, a Time-Gated Variance estimator linking finite-duration variance to the noise PSD, and an optimal calibration duration obtained by balancing statistical precision against contamination from colored receiver noise. It then proposes a fully white SNC in which the white parts of receiver and electronic noise are separated spectrally and the shot-noise estimate is defined by

$T$5

Because this estimator excludes colored LO noise from the SNU, the paper reports higher performance and higher tolerance to receiver imperfections than traditional SNC (Ricard et al., 9 Sep 2025).

Taken together, these works establish that SNC in CV-QKD is not merely a convenience for normalization. It is part of the trusted-noise model itself, and therefore part of the security proof.

6. Misconceptions, limitations, and related methods

Several recurrent misconceptions are corrected by the literature. First, Schottky noise is not simply a synonym for shot noise: the integrated power may be consistent with shot-noise theory, but the spectral pattern is a comb of revolution harmonics rather than a white floor (Chen, 2018). Second, noise measured with LO on is not automatically shot noise. In CV-QKD and coherent detection, LO RIN, receiver excess noise, and common-mode leakage can be mistaken for shot noise if the calibration model omits spectral structure or insufficient common-mode rejection (Ricard et al., 9 Sep 2025, Gurses et al., 8 Apr 2026). Third, SNC is not necessarily a one-off hardware characterization. In SCOS, small drifts in $T$6 and $T$7 can generate CBV-mimicking artifacts, motivating per-trace adaptive refinement (Liu et al., 18 Jun 2025).

The main technical limitations are equally consistent across domains. All derivations rely on explicit stochastic assumptions: Poisson statistics and independence in electronic shot noise, random initial phases in Schottky pickups, linear readout chains in substitution-based microwave calibration, and WSS in dynamic CV-QKD calibration. Violations include space charge, Coulomb interaction, bunching, coherent beam motion, wakefields, pump-activated nonlinear channels, imperfect impedance knowledge, finite resolution bandwidth, drift of readout gain, and nonstationary low-frequency noise. In imaging sensors, additional difficulties arise from ISP behavior that makes flat-field RAW frames less noisy than textured scenes at the same ISO, from non-monotonic manufacturer noise profiles, and from the sensor-dependent choice between Gaussian read-noise intercepts and empirically captured dark frames (Chen, 2018, Celotto et al., 27 May 2026, Ricard et al., 9 Sep 2025, Bhatt, 17 Dec 2025).

SNC also sits beside, rather than above, other absolute noise references. The cryogenic microwave literature explicitly presents thermal Planck-noise calibration with a Variable Temperature Stage as a conceptually related alternative to SNC, and emphasizes that the decisive issues are the predictable noise law, the placement of the source, and the coincidence of noise and scattering reference planes (Celotto et al., 27 May 2026). This suggests a general characterization of SNC: it is a calibration doctrine centered on physically modeled fluctuation laws, but its success depends at least as much on geometry, bandwidth, detector model, and reference-plane definition as on the universality of shot noise itself.