CHSH Across Witness Families: A Verifier That Doesn't Care About the Test
In our first post we walked through the anatomy of one verified quantum block — a Mermin(3) test on Rigetti Cepheus-1-108Q, statistic 2.685, 3.69σ above the classical bound, deterministically re-verifiable in a browser.
That post triggered exactly the question we hoped it would: is this specific to Mermin?
Fair question. Bell tests come in families. Mermin(3) is a three-party inequality. CHSH is the classical two-party Bell test. Svetlichny(3) is a stronger tripartite bound. And there are more — Bell(N), the Braunstein-Caves chained inequality, Salavrakos-family n-body correlators, GHZ-Mermin generalizations. Any credible verifier has to be witness-agnostic — the code path can't be baked to one specific test, or you've built a demo, not a protocol.
So we ran CHSH.
The block
CHSH is the original Bell test. Two parties, two settings each, four correlator groups (AB, AB', A'B, A'B'), classical bound of 2. Its quantum ceiling — the Tsirelson bound — is 2√2 ≈ 2.828, achieved on a Bell state |Φ+⟩ measured at optimal π/4-offset angles.
We prepared a Bell state on Rigetti Cepheus, ran 1024 shots across the four groups with challenge-bound measurement settings, and let the verifier do the same thing it does for Mermin: parse the anchor, rebuild the Merkle roots, compute the statistic from published outcomes as an exact rational, check against the declared classical bound.
Result: |S| = 128249/60515 ≈ 2.119. Above the classical bound of 2. FENCE PASS.
Cleared by ~0.12 — a smaller margin than the Mermin run, but a real violation, and honest hardware. Bell-state fidelity on Cepheus is roughly 75% at these gate depths; the 2.119 falls right where the physics would predict.
What changed on our side
Almost nothing.
- Same block-binding: the challenge that seeded CHSH's per-shot measurement settings is derived the same way as Mermin's — SHA-256 over (prev_chain_head, nonce, device_arn, n_shots, phenomenon).
- Same anchor format:
version,device_arn,program_hash,runs_root,settings_root,challenge,nonce,n,entry_hash. Thephenomenonfield is"CHSH"instead of"Mermin_3". Everything else identical. - Same verifier code: the browser doesn't care which witness it's verifying. It reads the witness spec (terms, coefficients, and classical bound) from the anchor's raw data, computes the statistic against those terms, and reports fence-pass or not.
- Same Merkle-root construction over the raw shots. Same challenge-binding audit. Same entry_hash preimage. Same exact-rational arithmetic.
The only thing witness-family-specific is the physics: CHSH needs a 2-qubit Bell state and π/4-offset rotations; Mermin needs a 3-qubit GHZ state and X/Y bases — different circuits, different quantum ceilings, different classical bounds. The verifier doesn't need to know any of that. It just runs the math the anchor tells it to run.
Try it
Go to qblex.com/verify. Click the CHSH · |S| 2.119 button. Watch the verifier recompute S = 128249/60515 in your browser from the 1024 published shot outcomes, rebuild the Merkle roots, and accept-or-reject against the classical bound of 2.
The same browser tab that verified the 2.685 Mermin now verifies a completely different Bell inequality with zero code changes. That's what witness-agnostic means.
What this proves
The verifier is a protocol, not a demo. It handles multi-witness verification because the mathematical structure of Bell-family inequalities is captured in the anchor itself — coefficients, per-party settings, classical bound. Everything downstream is generic arithmetic.
In the next post we'll take this further: we'll show what happens when we run a stronger Bell inequality — Svetlichny(3), which requires genuinely tripartite entanglement — on the same Cepheus hardware. It won't be a pretty story. And that's the point.
Don't trust us. Run the math.
QBLEX technologies are patent pending (U.S. App. Nos. 19/711,486; 19/702,980; 19/707,649 — priority June 2025). "Patent pending" does not indicate a granted patent.