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)\vec N_{\text{bit}}=(80,20)
Population changeThe bit-flip channel moves counts between labels.1zero0one4/5zero1/5onechannel map

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.

Nvisible=30N_{\text{visible}}=30
Separate phase budgetPhase loss is not relabeled as a bit flip.3/5coherent2/5dephasedphase loss