Classical pre-combination

Conditionally on the reference, encode ${\iota }_1(I_{\mathrm{rel}})$ with scale ${\sigma }_I>0$, and use $P_{\mathrm{read}}$. Its complete record, with unit quantum output, has law

It is invariant wherever $I_{\mathrm{rel}}$ is invariant and distinguishes different values of $I_{\mathrm{rel}}$ statistically. The scale ${\sigma }_I$ has the units of $I_{\mathrm{rel}}$.

All relational work occurs in the classical pre-combination. Enter supplies no new covariance identity. Informative here means dependence across different invariant values, not variation along one gauge orbit.