Perfect pure quantum state transfer via state restoring and ancilla measurement
We propose the protocol for perfect state transfer of an arbitrary pure quantum state along the spin-1/2 chain governed by the Hamiltonian preserving the excitation number in the system. We show that the $k$-excitation pure sender's state can be restored at the receiver using only the local transformations over the qubits of the extended receiver. The restored state appears in the superposition with other states which form garbage. This garbage can be easily removed by including the ancilla, whose state labels the garbage, and then measuring the {ancilla state} with desired output. The resulting state of the receiver coincides with the initial sender's state {up to the unimportant common phase factor.} Then, to transfer an arbitrary {pure} state of some system $S_0$, we encode this state into the $k$-excitation state of the sender, transfer and restore this state and finally decode the restored $k$-excitation state {of the receiver} into the state of another subsystem $R_0$. After labeling and removing the garbage via the ancilla-state measuring we complete the algorithm for the perfect transfer of an arbitrary pure state.