Intrinsic and recorded observables

Suppose the implemented self-adjoint observable, in the declared residual frame, satisfies

where

The bounded remainder preserves self-adjointness on the field domain. Let $n_{\sigma }=\mathrm{Tr}(\sigma N)<\infty$.

Let $X_j$ be its spectral outcome in $\sigma$. A recorded surrogate outcome $Y_j$ has a specified coupling

This representation may be independent additive detector noise or a certified correlated readout error.

Finally, if a physical carrier is claimed, require a same-quantity comparison between its recorded law ${{\nu }_j}^{\mathrm{bio}}$ and the surrogate recorded law:

Both laws must have finite second moments.