Bell State Generation
CNOT on |+⟩|0⟩ creates maximally entangled qubits
Bell States
Φ⁺
Φ⁻
Ψ⁺
Ψ⁻
|Φ⁺⟩ = (|00⟩ + |11⟩)/√2
|Φ⁺⟩
Measure!
Amplitudes
Each Bell state has equal 50/50 probability for its two outcomes, but the outcomes are
perfectly correlated
— measuring one qubit instantly determines the other.
CHSH Inequality
|S| = |⟨AB⟩+⟨AB'⟩+⟨A'B⟩−⟨A'B'⟩|
Classical bound: |S| ≤ 2
Quantum bound: |S| ≤ 2√2 ≈ 2.828
Bell states achieve the Tsirelson bound, proving
no local hidden variable theory
can reproduce these correlations.
|S|
2.83
Classical limit: — at 2.0