Definition: Represented instrument and external labels

With $P_z=|z⟩⟨z{|}_S\otimes I_B$, the represented nondestructive sharp instrument is

It can be implemented using a fresh pointer and destructive readout of that pointer. The original $S$ is returned.

An external geometric label is classical metadata describing a marking, chart, certificate, or location. A dictionary from measurement outcomes to such labels is an additional input. It is not one of the preceding quantum maps.