 Choi matrix

For normalized maximally entangled $|\varphi ⟩=d^{-1/2}{\sum }_j|jj⟩$, the Choi matrix of $T$ is $C_T=(T\otimes \mathrm{id})(|\varphi ⟩⟨\varphi |)$. Choi's theorem says $T$ is completely positive exactly when $C_T\ge 0$.