Measured Shot Scan - Quantum States & Qubits Step by Step

A finite batch of identically prepared systems turns squared amplitudes into expected measurement counts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Expected counts start with squared amplitudes

The rendered state uses amplitudes 3/5 and 4/5. Squaring gives probabilities 9/25 and 16/25.

P_{\text{zero}}=\frac{9}{25},\quad P_{\text{one}}=\frac{16}{25}

The first row has exact expected counts

For 25 identically prepared systems, the expected counts are 9 zero outcomes and 16 one outcomes. This is still an expectation, not a random draw.

N_{\text{zero}}=9,\quad N_{\text{one}}=16

Three states give three exact shot ledgers

Each row squares the two amplitudes and multiplies by the trial count. The last row uses more trials because thirteenths need a larger exact square denominator.

\begin{array}{c|c|c|c|c}a&b&N&N_{\text{zero}}&N_{\text{one}}\\\frac{3}{5}&\frac{4}{5}&25&9&16\\\frac{4}{5}&\frac{3}{5}&25&16&9\\\frac{5}{13}&\frac{12}{13}&169&25&144\end{array}

Counts do not replace the state update rule

The table audits the pre-measurement distribution. A particular measurement result still updates the next state, so this scan does not pretend that expected counts are hidden prewritten answers.

N_{\text{zero}}+N_{\text{one}}=N,\quad P_{\text{zero}}+P_{\text{one}}=1