Interfaces and complete preparation

Ideal and actual preparations are supplied as isometries into identified complete spaces, with every fixed auxiliary purification and preparation environment retained:

The ideal extended preparation appends field vacuum and declared purified fixed auxiliaries.

The actual full propagator must exist. On the ideal prepared retained sector, it obeys Theorem thm:C6. Any participating auxiliary coupling requires a checked perturbation allowance on that enlarged retained space. The preparation comparison may account for actual components outside the ideal sector because the first replacement below uses the actual full propagator.

Let ${\tilde{\mathcal{N}}}_{N,T}$ be the actual accessible channel under the same ideal packet factorization. Assume

and define

An imperfect physical collector can be inserted with its own accessible allowance $e_{\mathrm{collection}}$. The principal formula assumes the ideal packet-access interface; a physical collector is not silently supplied by Fock factorization.