Measurement

Measurement is where quantum becomes classical. Before measurement, a qubit exists in a superposition described by amplitudes. Measurement forces a definite outcome: 0 or 1. The probability of each outcome follows the Born rule: you square the magnitude of the amplitude. If the state is $\alpha$$|0⟩+\beta$$|1⟩$, the probability of getting 0 is |$\alpha$|² and the probability of getting 1 is |$\beta$|². After measurement, the qubit is in the state matching the result you observed. The superposition is gone, and you cannot recover it. This irreversibility is what makes measurement fundamentally different from every gate operation.

Measuring a superposition

1. 1Start with $H|0⟩=(|0⟩+|1⟩)/\sqrt{2}$. The qubit is in an equal superposition.
2. 2The amplitudes are $\alpha =1/\sqrt{2}$ and $\beta =1/\sqrt{2}$.
3. 3Apply the Born rule. Probability of 0: |$\alpha$|² = 1/2. Probability of 1: |$\beta$|² = 1/2.
4. 4Measurement returns either 0 or 1, each with 50% probability.
5. 5Suppose you get 0. The post-measurement state is $|0⟩$. The superposition is gone and cannot be recovered.
6. 6Repeating the entire preparation-then-measurement process many times confirms the 50/50 statistics.

Measurement is the only way to get information out of a quantum computer. All other operations (superposition, entanglement, interference) are preparation for the moment when measurement converts quantum amplitudes into classical data that you can read and use.