Definition: Finite classical-environment process class

Fix:

1. a quantum carrier of dimension $d$;

2. a classical environmental alphabet $\mathcal{E}=\{1,\dots ,L\}$;

3. a finite schedule and admitted laboratory interventions;

4. the controller and accessible-record rules.

Classical–quantum states have the form

At an environmental update, specify CP maps

on the carrier, with

trace preserving for each $e$. The update is

Dependence on admitted past settings and records must be specified through the declared controller.

The environment has no independent access to the encoded classical input unless such access is explicitly admitted. Initial environmental information is independent of the fresh input. Laboratory intervention records and persistent feedback are included in the complete process.