Path Labels Are The Physical State - Quantum Mechanics IV: Photons, Interferometers, and Optical Qubits Step by Step

In this optical model, upper and lower are physical path-state labels, not just drawing labels. The count ledger is exact only for the stated path labels and splitter output; real path measurements depend on alignment, mode matching, detector efficiency, phase stability, and background counts.

For this training model, the path label is the physical state label being counted. 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 paths are physical state labels

After the splitter, the upper label carries 4 counts and the lower label carries 4 counts.

N_{\text{upper}}=4,\quad N_{\text{lower}}=4

No single shot is predicted by the count ledger

The ledger says an ensemble of 8 photons splits into two path counts of 4 each.

N_{\text{upper}}=N_{\text{lower}}=4