CHSH Violation
Calculate CHSH S from four measured correlations.
Description
A CHSH statistic combines four supplied correlations under a fixed sign convention.
A CHSH statistic combines four supplied correlations under a fixed sign convention. A strict comparison with two flags the classical-bound exceedance.1
Calculate CHSH S from four measured correlations.
When to use CHSH Violation
Use this tool to calculate CHSH S from four measured correlations.
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 CHSH Violation 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 correlation00, correlation01, correlation10, correlation11 using the field table and calculation rules, then run the tool.
- Read chshS, violatesClassicalBound. 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 |
|---|---|---|---|
| correlation00 | Correlation E00 | number; minimum: -1; maximum: 1 | Required |
| correlation01 | Correlation E01 | number; minimum: -1; maximum: 1 | Required |
| correlation10 | Correlation E10 | number; minimum: -1; maximum: 1 | Required |
| correlation11 | Correlation E11 | number; minimum: -1; maximum: 1 | Required |
Enter correlations from −1 to one. Return S and flag; S=2 is unflagged.
S=|E00+E01+E10−E11|; violation=S>2 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| chshS | CHSH S value | number; minimum: 0 |
| violatesClassicalBound | Violates classical bound | boolean |
{
"input": {
"correlation00": 0.7,
"correlation01": 0.7,
"correlation10": 0.7,
"correlation11": -0.7
},
"output": {
"chshS": 2.8,
"violatesClassicalBound": true
}
}Limitations and assumptions
No uncertainty, measurement settings, loopholes or experiment validity are checked. Inputs can produce S up to four without quantum-realizability validation.
Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use HBT Correlation: Calculate normalized zero-delay HBT second-order correlation. For a complementary task, use Twin-Field PLOB Comparison: Compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound.
References
-
CHSH Violation — tool.io
Similar or alternative tools
- HBT Correlation
Calculate normalized zero-delay HBT second-order correlation.
- Twin-Field PLOB Comparison
Compare an achieved twin-field secret-bit rate with the repeaterless PLOB bound.