We show that the Hadamard and Unitary gates could be implemented by a unitary evolution together with a measurement for any unknown state chosen from a set $A = { { | { \Psi_i} > ,| { \bar { \Psi}_i} >}}({ i = 1,2})$ if and only if $| { \Psi_1} > ,| { \Psi_2} > ,| { \bar { \Psi}_1} > ,| { \bar { \Psi}_2} >$ are linearly independent. We also derive the best transformation efficiencies.
Categories: quant-ph
