  If $H_1$ and $H_2$ are finite-dimensional Hilbert spaces, a channel from
$H_1$ to $H_2$ is a completely positive, linear map $\mathcal{I}$ that takes
the set of states $\mathcal{S}(H_1)$ for $H_1$ to the set of states
$\mathcal{S}(H_2)$ for $H_2$. Corresponding to $\mathcal{I}$ there is a unique
dual map $\mathcal{I}^*$ from the set of effects $\mathcal{E}(H_2)$ for $H_2$
to the set of effects $\mathcal{E}(H_1)$ for $H_1$. We call $\mathcal{I}^*(b)$
the effect $b$ conditioned by $\mathcal{I}$ and the set $\mathcal{I}^c =
\mathcal{I}^*(\mathcal{E}(H_2))$ the conditioned set of $\mathcal{I}$. We point
out that $\mathcal{I}^c$ is a convex subeffect algebra of the effect algebra
$\mathcal{E}(H_1)$. We extend this definition to the conditioning
$\mathcal{I}^*(B)$ for an observable $B$ on $H_2$ and say that an observable
$A$ is in $\mathcal{I}^c$ if $A=\mathcal{I}^*(B)$ for some observable $B$. We
show that $\mathcal{I}^c$ is closed under post-processing and taking parts. We
also define the conditioning of instruments by channels. These concepts are
illustrated using examples of Holevo instruments and channels. We next discuss
measurement models and their corresponding observables and instruments. We show
that calculations can be simplified by employing Kraus and Holevo separable
channels. Such channels allow one to separate the components of a tensor
product.
