Bell Test Virtual Experiment (CHSH)

Optical table

Running

0 / 20,000

Experiment mode

Bell state

P_{++} = P_{--} = \frac{1}{2} cos^{2} (a - b), P_{+-} = P_{-+} = \frac{1}{2} sin^{2} (a - b)

Bell state |Φ⁺⟩ = (|HH⟩ + |VV⟩)/√2: the probabilities depend only on the angle difference, and at equal angles the results always agree.

Photon pairs sent (N)

In steps 3 and 4 the pairs are shared equally among the four angle combinations: N/4 each.

AliceA

λ/2 plate: 0°

BobB

λ/2 plate: 0°

Noise

The share of pairs whose results environmental factors scramble at random; the observed correlation shrinks in the same proportion.

Detection is ideal: no photon is lost, and every pair records one result for Alice and one for Bob.

Choose the source mode and send a few hundred pairs; then compare the measured probabilities with the formula.

For each angle combination: the number of pairs, the correlation E and the counts of the four outcomes ++, +−, −+ and −−
Setting	Trials	E	++	+−	−+	−−
(A, B)	0	—	0	0	0	0

Equal

Alice's and Bob's totals are equal (0 pairs): every pair gives one result to Alice and one to Bob.

For Φ⁺ equal results have probability ½cos²(a−b) and opposite results ½sin²(a−b).