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
Understand what a qubit is, how it differs from a classical bit, and be able to describe superposition and measurement in simple terms.
1.1 What is a Qubit?
A qubit is represented as a unit complex vector |ψ⟩ = α|0⟩ + β|1⟩ where α,β ∈ ℂ and |α|² + |β|² = 1.
classical bit: 0 or 1 quantum bit (qubit): α|0⟩ + β|1⟩, |α|²+|β|²=1
1.2 Superposition
When a qubit is in a superposition, it can be measured to collapse to |0⟩ or |1⟩ with probabilities |α|² and |β|² respectively.
|ψ⟩ = α|0⟩ + β|1⟩ Prob(0) = |α|², Prob(1) = |β|²
1.3 Measurement
Measurement forces the qubit into one of the basis states, destroying the superposition.
Measurement → collapse |ψ⟩ = α|0⟩ + β|1⟩ → 0 (prob |α|²) or 1 (prob |β|²)
Put it together
Worked example
Example: Prepare a qubit in the state |ψ⟩ = (1/√2)|0⟩ + (1/√2)|1⟩. Measuring this qubit yields 0 or 1, each with probability 0.5.
Key takeaways
• A qubit can represent 0 and 1 simultaneously. • Superposition is described by probability amplitudes. • Measurement collapses the state and yields a classical outcome.
Knowledge check / 3 questions