Preparation, loss, and joint capture error

This prices a common port, overlapping windows, and the nonvacuum background in one comparison. It does not assume that the two target packets or their environmental modes are independent.

For a non-Gaussian input, replace ${\mu }_L$ and $E_F$ by its justified participating-mode values. The same interaction and loss proof then apply.

Figure fig:capbudget prices preparation and storage once, on the joint memories. Unselected positive-frequency radiation stays in the input; it is not replaced by vacuum. The composite transmissivity is ${\tau }_{\ast }=\tau s$.