Beam Splitters as Path Ledgers

Path Labels Are The Physical State

upper and lower

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.

Nupper=4,Nlower=4N_{\text{upper}}=4,\quad N_{\text{lower}}=4
Path labelsUpper and lower are the checked physical labels.1/2upper1/2lowersplitter

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.

Nupper=Nlower=4N_{\text{upper}}=N_{\text{lower}}=4
Path count ledgerThe model is an ensemble count check.1/2upper1/2lowersplitter