Error budgets and sequential stability

A classical norm estimate is not automatically a diamond estimate. For classical intermediate maps with Lipschitz constants $L_i$, an error recursion

gives, by induction,

Converting this bound into ${ϵ}_{\mathrm{adiabatic}}$ requires a theorem relating that classical norm to the selected field state or complete channel. The source-input stability estimates in Em06-B and the interface allowances in En03-A are relevant precedents, not substitutes for that theorem CheungEm06B,CheungEn03A.