Amplitude to Probability - Quantum States & Qubits Step by Step

Measurement probabilities come from squared amplitudes, not from the amplitudes themselves. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Amplitude is not probability

The zero amplitude is 3/5, but the zero probability is the square: 9/25.

\left(\frac{3}{5}\right)^{2} = \frac{9}{25}

The other outcome is squared too

The one amplitude is 4/5, giving probability 16/25.

\left(\frac{4}{5}\right)^{2} = \frac{16}{25}

Squaring changes the scale

The same square rule is shown for three exact amplitudes. The middle two rows are the amplitudes in the diagram.

\begin{array}{c|c}a&P\\\frac{1}{5}&\frac{1}{25}\\\frac{3}{5}&\frac{9}{25}\\\frac{4}{5}&\frac{16}{25}\end{array}