Entangled Asset Correlation: Quantum Bell Test for Portfolio Risk

Measurement Settings

Asset A angle θ_A 0°

Asset B angle θ_B 22°

Trial rate 6 / s

Live Correlation

E(θ_A,θ_B) — active model

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Trials run

CHSH statistic S 0.00

0classical ≤ 2quantum ≤ 2√2 ≈ 2.83

S — quantum pair (bkg)

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S — classical pair (bkg)

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How it works

Two "assets" receive a correlated shock every trial. This models the article's claim that entangled assets are linked "beyond statistical correlation" — tested the same way physicists test real entanglement, with a Bell/CHSH experiment.

Quantum (singlet) trial:
  outcome A = ±1 with 50/50 probability
  P(B=A | θA,θB) = sin²((θA−θB)/2)
  → Monte-Carlo sampled every trial
  E_quantum(θA,θB) → −cos(θA−θB)  as trials→∞

Classical (local hidden variable) trial:
  hidden state λ ~ Uniform(0°,360°)
  A = sign(cos(θA−λ)),  B = −sign(cos(θB−λ))
  → deterministic function of shared λ only
  E_classical(θA,θB) → bounded, never beats CHSH ≤ 2

CHSH statistic (angles fixed at the textbook-optimal
0°, 45°, 22.5°, 67.5° in the background):
  S = E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′)

θ_A / θ_B sliders — the "analysis angle" each asset's shock is measured against; drive the live E(θA,θB) readout and the front-panel visualization.
Quantum / Classical pair — switches which model drives the two glowing spheres and the outcome flashes, so you can watch the same angles produce different correlation strength.
CHSH S — accumulated in the background from real Monte-Carlo trials of both models at the fixed optimal angles, independent of the sliders above. The quantum pair's S climbs toward 2√2 ≈ 2.83; the classical pair can never cross S = 2 — exactly the gap the article's "R(A,B) > 1" claim is trying to describe mathematically.

This is the real CHSH inequality used to certify entanglement in physics labs, applied here as a concrete, testable stand-in for the vague claim that "entangled" assets share fate beyond ordinary covariance.

Outcome +1 Outcome −1 Entanglement link

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