Operational boundary

The enlarged construction specifies interval maps, fresh ancillary inputs, complete instruments, and all persistent registers. At a fixed current setting, its next update depends on the current enlarged state. Any controller memory needed for future update choices must also be included.

This is a Markov construction. A family of one-time reduced CPTP maps does not by itself establish operational Markovianity. Pollock and colleagues formulate the relevant test using measurement followed by re-preparation: after a causal break, the conditional future must be independent of past carrier controls and outcomes for a Markov process PollockMarkov,PollockProcess.

Let

reset the carrier while leaving the scar register untouched. For a classical–quantum state,