Population motion and phase visibility are different exact budgets. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A bit-flip budget changes population counts
The population channel changes the state ledger from 100 zero shots to 80 zero and 20 one.
Nbit=(80,20)
A phase-loss budget changes visible signal instead
The phase-loss budget keeps the question as visibility: 50 ideal visible counts reduce to 30 visible counts.