Optimal transfer of an unknown state via a bipartite operation

A fundamental task in quantum information science is to transfer an unknown state from particle $A$ to particle $B$ (often in remote space locations) by using a bipartite quantum operation $mathcal{E}^{AB}$. We suggest the power of $mathcal{E}^{AB}$ for quantum state transfer (QST) to be the maximal average probability of QST over the initial states of particle $B$ and the identifications of the state vectors between $A$ and $B$. We find the QST power of a bipartite quantum operations satisfies four desired properties between two $d$-dimensional Hilbert spaces. When $A$ and $B$ are qubits, the analytical expressions of the QST power is given. In particular, we obtain the exact results of the QST power for a general two-qubit unitary transformation.