Improving fidelity of quantum cloning via the Dzyaloshinskii-Moriya interaction in a spin network

We investigate the effect of the Dzyaloshinskii-Moriya (DM) interaction on the fidelity of the 1 -> M phase-covariant cloning machine (PCCM) in a spin star network. The results of numerical calculation show that the DM interaction can further improve the cloning fidelity to reach the optimal value. Furthermore, the physical mechanism is investigated by analyzing the effect of the DM interaction on the populations of the qubits. It is shown that the DM interaction leads to the populations of states vertical bar 1 >vertical bar S(M, k + 1)> and vertical bar 1 >vertical bar S(M, k)> [or vertical bar 0 >vertical bar S(M, k)> and vertical bar 0 >vertical bar S(M, k -1)>] simultaneously reaching the maximum or minimum value periodically, where the first ket vertical bar i > (i is an element of 0,1) in vertical bar i >vertical bar S(M, k)> denotes the state of central spin with vertical bar 0 > and vertical bar 1 > representing the spin-up and spin-down states, respectively, while the second ket vertical bar S(M, k)> denotes the state of outer spins with M being the total number of outer spins and k the number of up spins. At these extreme overlapping points of two states, the fidelity of quantum cloning can reach optimal value. Finally the forms of these two different 1 -> M optimal cloning transformations are presented.