Start with eight toy photons entering an interferometer that splits them into
two equal arms. When the path phases match, the two arms recombine into the
bright detector, so the pinned count ledger is 8 bright and 0 dark; a real
interferometer still depends on alignment, phase drift, loss, and detector
efficiency.
The same-phase interferometer case keeps the full count budget at the bright detector. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The first splitter creates two equal arms
The incoming count 8 first splits into 4 upper and 4 lower.
8→4+4
Same phase recombines at the bright detector
With same phase, the recombined output is 8 bright counts and 0 dark counts.