Your objective
Understand how measurement works on single and multi‑qubit states, the effect on superposition, and how measurement can be used to extract information without destroying the entire quantum computation.
3.1 Projective Measurement in the Computational Basis
Measuring in the {|0⟩,|1⟩} basis yields outcome 0 with probability |α|² and 1 with probability |β|².
Outcome 0 (prob |α|²) Outcome 1 (prob |β|²)
3.2 Measurement in Arbitrary Basis
A measurement can be performed in any orthonormal basis {|ϕᵢ⟩}. The probabilities are |⟨ϕᵢ|ψ⟩|².
Prob(ϕᵢ) = |⟨ϕᵢ|ψ⟩|²
3.3 Effect on Entanglement
Measuring one particle of an entangled pair collapses the joint state, instantaneously fixing the partner's state in the chosen basis.
Entangled pair → measure qubit A → qubit B collapses to correlated state
Put it together
Worked example
Measure the Bell state (|00⟩ + |11⟩)/√2 in the computational basis. Result 00 occurs with 50% probability, collapsing the state to |00⟩; result 11 collapses it to |11⟩.
Key takeaways
• Measurement is basis‑dependent. • Outcomes are probabilistic, given by squared amplitudes. • Measuring one qubit of an entangled pair instantly determines the other's state.
Knowledge check / 3 questions