Definition: Conditional endpoint package

An endpoint package for the fixed code supplies:

1. A justified complete pure preparation $P_0:C\to H_{\mathrm{tot}}$.

2. A specified input-independent unitary evolution $U_t$ on that complete system, on a justified time domain.

3. Output identifications $F_t:H_{\mathrm{tot}}\to R_t\otimes B_t$, factorwise isometries

   $$a_t:R_t\to R_{\ast },b_t:B_t\to B_{\ast },$$

   and an endpoint isometry $V_{\ast }:C\to R_{\ast }\otimes B_{\ast }$ such that

   $$V_t=(a_t\otimes b_t)F_t{U}_t{P}_0,{\nu }_t=\min \{1,{\Vert V_t-V_{\ast }\Vert }_{\infty }\}⟶0.$$

   The comparison maps preserve the access roles.

4. A state ${\sigma }_{\ast }\in \mathcal{D}(B_{\ast })$ and a proved bound

   $$d_{\diamond }({\mathcal{E}}_{\ast },{\mathcal{T}}_{{\sigma }_{\ast }})\le \zeta ,{\mathcal{E}}_{\ast }={\mathrm{Tr}}_{R_{\ast }}{\mathrm{Ad}}_{V_{\ast }}.$$

For physical application, these data must be justified within one compatible microscopic model.