A state you can explore.
Interactive / 01Measurement probabilities
For this real-amplitude family, |ψ⟩ = cos(θ/2)|0⟩ + sin(θ/2)|1⟩. Change θ to redistribute the measurement probabilities.
A measurement returns one outcome. The bars show probabilities, not two physical objects.
Your objective
Grasp how superposition enables a qubit to process multiple states at once and understand the mathematical representation of multiple‑qubit superpositions.
2.1 Single‑Qubit Superposition
Any single qubit state is α|0⟩ + β|1⟩ with normalization condition.
|ψ⟩ = α|0⟩ + β|1⟩, |α|²+|β|²=1
2.2 Multi‑Qubit States
The state of n qubits lives in a 2ⁿ‑dimensional Hilbert space, described by the tensor product of individual qubit states.
n‑qubit state = |ψ₁⟩ ⊗ |ψ₂⟩ ⊗ … ⊗ |ψₙ⟩
2.3 Measurement Probabilities
When measuring a multi‑qubit state, the probability of each basis outcome is the squared magnitude of its amplitude.
Probability of |101⟩ = |α₁₀₁|²
Put it together
Worked example
Create a 2‑qubit superposition (|00⟩ + |11⟩)/√2. This is an entangled Bell state (see Module 4).
Key takeaways
• The state space grows exponentially with qubit count. • Tensor products combine individual qubit states. • Measurement extracts a single basis outcome probabilistically.
Knowledge check / 3 questions