A measurement result updates the state used for repeat measurements. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Measurement uses the probability distribution

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

Nzero=9,None=16N_{\text{zero}} = 9,\quad N_{\text{one}} = 16
Measurement updateThe distribution is exact before the update.9/25zero16/25onestate3/5 zero4/5 onestate1 zero0 oneafter measurement

After a result, the state updates

After the zero result, a repeat measurement of the updated state gives zero with probability 1.

P(zero after zero)=1P(\text{zero after zero}) = 1
Measurement updateThe post-measurement state is the zero basis state.9/25zero16/25onestate3/5 zero4/5 onestate1 zero0 oneafter measurement

Expected counts scale with trials

The probability distribution is fixed by the state. More identically prepared trials scale both expected counts in the same ratio.

NNzeroNone259165018321003664\begin{array}{c|c|c}N&N_{\text{zero}}&N_{\text{one}}\\25&9&16\\50&18&32\\100&36&64\end{array}
Measurement updateThe distribution bars stay the same while counts scale.9/25zero16/25onestate3/5 zero4/5 onestate1 zero0 oneafter measurement