Corollary: Sector and complete-experiment budgets

For bounded sector generators with CPTP propagators,

For two complete feedback experiments with initial-state error $e_{\mathrm{init}}$ and full interval or recorded-instrument errors $e_1,\dots ,e_m$, the final complete-record trace distance is at most

This also bounds final record total variation.

Proof. Apply the bounded-generator variation-of-constants interface in Psy03-A prop:dynamic and Psy02-B prop:dynamic, on the enlarged common spaces CheungPsy03A,CheungPsy02B. Channel composition contracts the diamond norm Watrous. A telescoping sum for complete recorded maps gives the second allowance.