Let $X$ be an operator system. We denote the set of all unital completely positive maps from $X$ to $M_{n}(\mathbb{C})$ by $UCP_{n}(X)$. How can I characterize $UCP_{n}(M_{n}(\mathbb{C}))$ or $UCP_{n}(C([0,1],\mathbb{C}))$?
For example, is there any relationship between $UCP_{n}(M_{n}(\mathbb{C}))$ and the unitary group of $M_{n}(\mathbb{C})$ or between $UCP_{n}(C([0,1],\mathbb{C}))$ and $M([0,1])$ (i.e. the set of all Borel measures on [0,1])?