Which entangled state

Where the pairs come from

Step through the circuit

Bars show the four amplitudes of the two-qubit state. Bar height is the amplitude and can be negative; the label is its probability (amplitude²).

Measurement dials

🎯 Use the settings that break the limit

Angles are the direction of the spin measurement (Bloch-sphere angle). For photons the polarizer turns half as far.

Run the experiment

〰 Sweep Bob's dial (all angles) 📨 Send Alice's results to Bob 🔄 Clear results

Sources

1. J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195 (1964). doi
2. Clauser, Horne, Shimony & Holt, “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23, 880 (1969). doi
3. B. S. Cirel’son (Tsirelson), “Quantum generalizations of Bell’s inequality,” Lett. Math. Phys. 4, 93 (1980). The 2√2 ceiling. doi
4. Hensen et al., “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682 (2015). Measured S = 2.42 ± 0.20 over 245 trials. doi
5. Nobel Prize in Physics 2022: Aspect, Clauser and Zeilinger, for experiments with entangled photons. press release

Every number on this page is computed live in your browser. The quantum outcomes are sampled from the Born rule on the exact two-qubit state. The “local model” is one explicit local hidden-variable model: each pair carries a single shared hidden direction. Bell’s theorem covers every local model, not only this one.