Measurement

Measurement is where quantum meets classical. Before measurement, a qubit exists in a superposition of possibilities described by amplitudes. Measurement forces a definite outcome: 0 or 1. The probability of each outcome is determined by the Born rule — you square the magnitude of the amplitude. After measurement, the qubit is in the state corresponding to the result you observed. All the superposition information is gone. This irreversibility is what makes measurement fundamentally different from any gate.

Measuring a superposition

1. 1Start with H|0⟩ = (|0⟩ + |1⟩)/√2.
2. 2The amplitudes are α = β = 1/√2.
3. 3Probability of 0: |α|² = 1/2. Probability of 1: |β|² = 1/2.
4. 4Measurement returns 0 or 1, each with 50% probability.
5. 5If you got 0, the post-measurement state is |0⟩. The superposition is gone.
6. 6Repeating the preparation and measurement many times confirms the 50/50 statistics.

Measurement is the only way to get information out of a quantum computer. Everything else — superposition, entanglement, interference — is preparation for the moment when measurement converts quantum amplitudes into classical data.