A swap mirror is modeled here as a clean exchange of the upper and lower rail labels. Starting from logical zero, the checked swap sends the occupied upper rail to the lower rail, and starting from logical one it sends the lower rail to the upper rail. Real mirrors and path routing add loss, alignment error, phase shifts, detector limits, and uncertainty that this exact label ledger deliberately leaves visible.
A checked swap exchanges the upper and lower rail labels. 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 swap sends upper occupation to the lower rail
Starting from logical 0, the checked swap gives output logical 1.
0swap1
The same swap sends lower occupation to upper
Starting from logical 1, the checked swap gives output logical 0.