Your objective
Identify entangled states, generate and recognize Bell states, and understand how entanglement enables quantum correlations stronger than any classical correlation.
4.1 What is Entanglement?
A pure state of two qubits is entangled if it cannot be written as a product of two single‑qubit states.
Entangled: (|00⟩ + |11⟩)/√2 (cannot be factored)
4.2 Bell States
The four maximally entangled two‑qubit states: |Phi⁺⟩, |Phi⁻⟩, |Psi⁺⟩, |Psi⁻⟩.
|Phi⁺⟩ = (|00⟩ + |11⟩)/√2 |Phi⁻⟩ = (|00⟩ - |11⟩)/√2 |Psi⁺⟩ = (|01⟩ + |10⟩)/√2 |Psi⁻⟩ = (|01⟩ - |10⟩)/√2
4.3 Measuring Bell States
Measuring in the computational basis distinguishes only two of the four Bell states. Full discrimination requires additional basis rotations.
Result 00 → |Phi⁺⟩ or |Phi⁻⟩ Result 01 → |Psi⁺⟩ or |Psi⁻⟩
Put it together
Worked example
Generate |Phi⁺⟩ by applying a Hadamard to qubit 0, then a CNOT with qubit 0 as control and qubit 1 as target, starting from |00⟩.
Key takeaways
• Entanglement creates correlations that cannot be explained classically. • Bell states are the canonical maximally entangled two‑qubit states. • Measurement outcomes reveal which Bell state was prepared only probabilistically.
Knowledge check / 3 questions