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CHSH Bell Inequality / S-Parameter Calculator
x402
CHSH Bell Inequality / S-Parameter Calculator is a paid API for AI agents from quantum.halowerk.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-14).
Converts raw coincidence counts (++, +−, −+, −−) for four measurement settings into CHSH correlators and computes the S parameter to test Bell inequality violation.
Price / call$0.004
Success—
StatusUnknown
How this service works
Converts ++, +−, −+ and −− counts into a correlation for each of AB, AB′, A′B and A′B′, then computes S = E(AB) + E(AB′) + E(A′B) − E(A′B′). A value above the classical bound in supplied data does not by itself demonstrate entanglement or close detection, locality, sampling or significance loopholes.
Output
Returns the four per-setting correlations E(AB), E(AB′), E(A′B), E(A′B′) derived from the coincidence counts, and the combined CHSH S value computed as E(AB) + E(AB′) + E(A′B) − E(A′B′). The response also indicates whether S exceeds the classical bound of 2, though the service notes that exceeding the bound alone does not close experimental loopholes such as detection, locality, or sampling loopholes.
Example use cases
Verifying photon entanglement experiment
“I just finished a photon coincidence experiment and need to check my CHSH S value. Here are the counts: AB is 600 ++, 50 +−, 48 −+, 602 −−; AB′ is 580 ++, 70 +−, 68 −+, 582 −−; A′B is 590 ++, 60 +−, 62 −+, 588 −−; A′B′ is 65 ++, 585 +−, 583 −+, 67 −−. Compute the correlators and the S parameter so I can see if it violates the Bell inequality.”
Classroom quantum mechanics demonstration
“For our quantum mechanics class demo I have these simulated coincidence counts for the four CHSH settings — AB: 300 ++, 200 +−, 200 −+, 300 −−; AB′: 280 ++, 220 +−, 220 −+, 280 −−; A′B: 290 ++, 210 +−, 210 −+, 290 −−; A′B′: 210 ++, 290 +−, 290 −+, 210 −−. What is the CHSH S value and does it go above the classical bound of 2?”
Benchmarking quantum hardware correlations
“I want to benchmark entanglement quality on a quantum processor. The coincidence counts from my Bell test run are: AB 8500 ++, 1500 +−, 1520 −+, 8480 −−; AB′ 8200 ++, 1800 +−, 1820 −+, 8180 −−; A′B 8300 ++, 1700 +−, 1720 −+, 8280 −−; A′B′ 1700 ++, 8300 +−, 8320 −+, 1680 −−. Please calculate all four E correlators and the S parameter.”
Technical details
Endpoint
POSThttps://quantum.halowerk.com/v1/entanglement-testWhen to prefer
Use this endpoint when you have raw coincidence count data from a Bell test experiment across all four CHSH measurement settings and need the S parameter quickly without implementing the correlator arithmetic yourself. It is ideal for physics research pipelines, quantum hardware benchmarking, educational demonstrations, and automated experiment analysis workflows. Prefer it over general-purpose math APIs because it encodes the precise CHSH formula (E(AB) + E(AB′) + E(A′B) − E(A′B′)) and handles the four-setting structure natively.
Side effects
- Fewer or more than exactly 4 measurement items returns a validation error
- Invalid or duplicate setting enum values cause rejection
- All counts zero for a setting produces a divide-by-zero or NaN correlation
- Negative count values are rejected by schema minimum constraint
- Counts exceeding 10^12 are rejected by schema maximum constraint
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| measurements | array |
Tags
x402
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