Universal existence of exact quantum state transmissions in interacting media

We consider an exact state transmission, where a density matrix in one information processor A at time $t=0$ is exactly equal to that in another processor B at a later time. We demonstrate that there always exists a complete set of orthogonal states, which can be employed to perform the exact state transmission. Our result is very general in the sense that it holds for arbitrary media between the two processors and for any time interval. We illustrate our results in terms of models of spin, fermionic, and bosonic chains. This complete set can be used as a basis to study the perfect state transfer which is associated with degenerate subspaces of this set of states. Interestingly, this formalism leads to a proposal of perfect state transfer via adiabatic passage, which does not depend on the specific form of the driving Hamiltonian.