Measure the correlation of a singlet entangled pair at different measurement angles and verify E(a,b)=−cosΔθ — the quantum curve, which no local hidden-variable model can reproduce when the CHSH combination S is computed against its classical bound of 2.
Advanced
Equipment
Virtual singlet entangled-photon source
Two polarization measurement channels with relative-angle slider Δθ
Pause button; readout $E(a,b)=-\cos\Delta\theta$
Procedure
Measure the correlation at one angle
Set the relative-angle slider Δθ to 0: the readout gives E=−cos0=−1 — the two sides always record opposite outcomes, the signature of the singlet ∣ψ−⟩=(∣01⟩−∣10⟩)/2.
Sweep the angle and trace the cosine
Raise Δθ through π/4, π/2, π and read E each time: −cos(π/4)≈−0,71, −cos(π/2)=0, −cosπ=+1. Compare with a local hidden-variable model, which only allows a straight-line (piecewise linear) correlation.
Estimate the CHSH combination
At the standard CHSH angles (0, π/4, π/2, 3π/4) read the four E values and compute S=E(a,b)+E(a,b′)+E(a′,b)−E(a′,b′). For the singlet S=22≈2,83>2, beyond the classical limit — illustrating why real Bell tests rule for quantum mechanics.
Simulation
Experiment history
In 1935 Einstein, Podolsky, and Rosen argued that quantum mechanics was incomplete because entanglement seemed to allow 'spooky action at a distance'; Niels Bohr rebutted the same year. John Stewart Bell turned the philosophical dispute into measurable numbers: in 1964 he proved any local hidden-variable theory must obey an inequality that quantum mechanics violates.
John Clauser measured entangled-photon correlations in 1972 and found the inequality violated; in 1982 Alain Aspect switched measurement settings faster than light could travel between the stations. Anton Zeilinger closed remaining 'loopholes' from 1998, and 'loophole-free' tests in 2015 ended nearly a century of debate — Clauser, Aspect, and Zeilinger shared the 2022 Nobel Prize.