Probabilistic implementation of universal Hadamard and Unitary gates

Abstract

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.