(color online)Experimental results. Panels (a1) and (a2) are the simulations of and , respectively. Panels (a3) and (a4) are the output of under and operations, respectively. We can learn the parity of the permutation by observing the difference between Panels (a3) and (a4). Panel (b) shows the fidelities of the the final states under the four operations in which cases the states are unchanged, the fidelities tend to identity. Panel (c) shows the fidelities of the the final state under the four operations in which case the states are changed to their quadrature states, the fidelities tend to zero.