  We study the dynamical properties of a strongly scrambling quantum circuit
involving a projective measurement on a finite-sized region by studying the
operator entanglement entropy and mutual information (OEE and BOMI) of the dual
operator state that corresponds to this quantum circuit. The time-dependence of
the OEE exhibits a new dynamical behavior of operator entanglement, namely an
additional fractional coefficient that accompanies the linear time growth of
the OEE. For a holographic system, this is equivalent to an additional
fractional coefficient that modifies the linear growth rate of the wormhole
volume. The time-dependence of the BOMI shows that the projective measurement
may destroy the non-local correlations in this dual state. We also propose a
gravity dual as well as a line-tension picture, which is an effective model,
that describe this strongly scrambling quantum circuit.
