Homodyne Quadrature Statistics
Calculate mean and population variance for shot-noise-normalized homodyne quadratures.
Description
Homodyne sample statistics report mean and population variance.
Homodyne sample statistics report mean and population variance. The shot-noise-units output equals variance and assumes upstream normalization.1
Calculate mean and population variance for shot-noise-normalized homodyne quadratures.
When to use Homodyne Quadrature Statistics
Use this tool to calculate mean and population variance for shot-noise-normalized homodyne quadratures.
Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
How to use Homodyne Quadrature Statistics and understand its results
- Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
- Enter quadratureSamples using the field table and calculation rules, then run the tool.
- Read meanQuadrature, variance, shotNoiseUnits. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| quadratureSamples | Homodyne quadrature samples | list of number | Required |
Enter nonempty finite quadrature samples. Return mean, variance and identical shotNoiseUnits value; one sample has zero variance.
mean=Σx/n; variance=Σ(x−mean)²/n Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| meanQuadrature | Mean quadrature | number |
| variance | Population variance | number; minimum: 0 |
| shotNoiseUnits | Variance in shot-noise units | number; minimum: 0 |
{
"input": {
"quadratureSamples": [
-1,
1,
-1,
1
]
},
"output": {
"meanQuadrature": 0,
"variance": 1,
"shotNoiseUnits": 1
}
}Limitations and assumptions
No homodyne acquisition, shot-noise calibration, entropy or squeezing significance is established.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use QRNG Sample Bit Extractor: Threshold supplied vacuum-noise samples into a deterministic bit sequence for downstream randomness testing. For a complementary task, use HBT Correlation: Calculate normalized zero-delay HBT second-order correlation.
References
-
Homodyne Quadrature Statistics — tool.io
Similar or alternative tools
- QRNG Sample Bit Extractor
Threshold supplied vacuum-noise samples into a deterministic bit sequence for downstream randomness testing.
- HBT Correlation
Calculate normalized zero-delay HBT second-order correlation.