Manuscript VII-J-ST@1 · VII-J-ST.tex · proposition · f1f1d82c
Proposition: Complete-channel error ledger
Approximate simulation and the Hamiltonian comparison · lines 1077–1096 · proof included or linked
VII-J-ST@1#prop:telescope
For compatible sequences of channels,
Every encoding, clock, controller, transition, communication, decoding, and failure output must be compared on matching interfaces.
Proof. Replace one factor at a time. The resulting telescoping sum has one channel difference in each term. Composition with channels contracts the diamond norm. Use the triangle inequality and divide by two.
Displayed formulas in this passage
unlabeled · line 1080