Measuring |+⟩

Measurement in the computational basis turns amplitudes into outcome probabilities through the Born rule: the chance of seeing outcome $b$ is $|\langle b|\psi\rangle|^2$.

For the equal superposition

$|+\rangle = \tfrac{1}{\sqrt{2}}\big(|0\rangle + |1\rangle\big),$

both amplitudes have magnitude $\tfrac{1}{\sqrt{2}}$, so

$P(0) = \left|\tfrac{1}{\sqrt{2}}\right|^2 = \tfrac{1}{2}, \qquad P(1) = \tfrac{1}{2}.$

A single measurement still yields a definite 0 or 1; the 50/50 split only shows up over many repetitions (shots).

Try it

Prepare $|+\rangle$ and measure it. The grader checks the probability distribution, which should be even across 0 and 1.

Open the Probabilities tab to see the two equal bars.

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