are down (up). In such states there is no SU(2) symmetry and one can split their degeneracy by applying a small magnetic field in the $z$ direction to choose one the ground states. Due to the absence of the SU(2) symmetry the fidelity of state transfer in both restricted and unrestricted basis depends on input parameter $\theta$. So, to quantify the quality of state transfer we consider a system of length $N$ initially prepared in one of its ground states, let say $|GS_\uparrow\ra$. Then a restricted measurement in $\sigma^z$ basis is performed on the first spin of the chain which projects the first qubit on either spin $\uparrow$ or spin $\downarrow$. Depending on the outcome of the measurement a further application of $R_\uparrow$ or $R_\downarrow$ rotates the first spin into $|\psi^{(+1)}\ra$ and initialization process is accomplished. A further time evolution of the system transfers this quantum states through out the chain. Just as before one can trace out the state of all spins but the last one and get the reduced density matrix of the last site $\rho_N(t)$ from which the fidelity is computed just as in Eq. (\[fid\_r\_ud\_t\]). To have an input independent quantity one can also average over 