Quantum entanglement simulation
Two entangled qubits share one quantum state that cannot be split into a state for each. This simulation walks the family cos α|00⟩ + sin α|11⟩ from no entanglement to the maximally entangled Bell state |Φ⁺⟩.
Interactive, free and runs in your browser. Part of the Quantum Mechanics simulations.
What you will see
Two qubits, each with its own Bloch vector. As you increase α the concurrence, a measure of entanglement, rises from 0 to 1, while each qubit’s Bloch vector shrinks towards the centre: a maximally entangled qubit has no definite state of its own, yet the pair’s results are perfectly correlated.
Try this
- Start at α = 0 and confirm each qubit is simply |0⟩.
- Move α to π/4 and watch both Bloch vectors shrink to zero length.
- Stop halfway and compare the concurrence with the vector lengths.
Common misconception
Entanglement cannot send a message faster than light. Each qubit on its own looks completely random; the correlation only appears when the two sets of results are compared, which needs an ordinary signal.
Exam-style question
For |ψ⟩ = cos α|00⟩ + sin α|11⟩ with α = π/4, what is the probability that both qubits are measured as 1, and what result can never occur?
P(11) = sin²(π/4) = 0.5. The outcomes 01 and 10 have zero amplitude, so the two qubits always agree: either both 0 or both 1.
Key equations
|Φ⁺⟩ = (|00⟩ + |11⟩)/√2C = |sin 2α|
Curriculum
AQA A-level physics, IB Physics HL C.3 and E.1.