  Random Clifford circuits doped with non Clifford gates exhibit transitions to
universal entanglement spectrum statistics[1] and quantum chaotic behavior. In
[2] we proved that the injection of $O(n)$ non Clifford gates into a $n$-qubit
Clifford circuit drives the transition towards the universal value of the
purity fluctuations. In this paper, we show that doping a Clifford circuit with
$O(n)$ single qubit non Clifford measurements is both necessary and sufficient
to drive the transition to universal fluctuations of the purity.
