Quantum entanglement

Compare Alice and Bob’s random local results and reveal correlations that violate a Bell inequality—without enabling faster-than-light messages.

Singlet state |Ψ⁻⟩ · optimal CHSH settingsRunning

AliceBob+1−1

Pairs emitted0

Coincidences0

Alice +0.0%

Bob +0.0%

Measured CHSH S—

Quantum prediction2.828

Correlation by setting pair

Joint outcomes

No-signalling: Alice’s local + rate

Random here, correlated together

Alice and Bob each see unpredictable +1 and −1 results. Only after matching records by pair and setting do the angle-dependent correlations emerge.

What Bell–CHSH tests

Local hidden-variable models obey S≤2. Quantum theory predicts up to 2√2. A simulated value above 2 rejects the tested local model, not logic, causality or all possible realism.

No faster-than-light message

Bob cannot control his random result, and changing his setting does not change Alice’s local 50/50 statistics. Entanglement supplies correlations, not a communication channel.

Scientific note: Joint outcomes are sampled from the singlet correlation E(a,b)=−cos(a−b), with visibility modelling depolarising noise. Paths are schematic and this educational simulation does not close real experimental loopholes.