A complete finite-shot certificate

Fix a stationary $n$-qubit implemented channel $\Phi$. Prepare $|{\Omega }_d⟩$, apply $\Phi$ to one half, and measure the resulting $2n$-qubit Choi state $\omega =J_{\mathrm{n}}(\Phi )$. Let

be that state's Hilbert-space dimension. Let $\mathcal{P}$ be the $D^2$ tensor-Pauli observables, including identity.