Born rule

The rule that measurement probabilities are given by squared amplitude magnitudes in the measurement basis.

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The Born rule connects the math of amplitudes to the reality of measurement outcomes.

Informal statement

If a state has amplitude $\alpha$ on an outcome, then the probability of that outcome is $|\alpha|^2$ .

Why it matters

It explains why quantum programs produce distributions rather than deterministic outputs.
It’s why shots are needed to estimate probabilities.

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