  The concept of $\e$-randomizing quantum channels has been introduced by
Hayden, Leung, Shor and Winter in connection with approximately encrypting
quantum states. They proved using a discretization argument that sets of
roughly $d \log d$ random unitary operators provide examples of such channels
on $\C^d$. We show that a simple trick improves the efficiency of the argument
and reduces the number of unitary operators to roughly $d$.
