Representing a von Neumann measurement as $[mathcal{I} otimes P_i] U(rho_s otimes rho_a)U^{-1} [mathcal{I} otimes P_i]$, how do we choose $U$?

Given the state of a system as $rho_s$ and that of the ancilla (pointer) as $rho_a$, the Von-Neumann measurement involves entangling a system with ancilla and then performing a projective measurement on the ancilla. This is often represented as
$$[mathcal{I} otimes P_i] U(rho_s otimes rho_a)U^{-1} [mathcal{I} otimes P_i],$$
where $mathcal{I}$ is the identity on system space, $P_i$ is the projector corresponding to $i$-th outcome, and $U$ is the combined unitary.

My question: How to choose the form of $U$?