  When subject to a non-local unitary evolution, qubits in a quantum circuit
become increasingly entangled. Conversely, measurements applied to individual
qubits lead to their disentanglement from the collective system. The extent of
entanglement reduction depends on the frequency of local projective
measurements. A delicate balance emerges between unitary evolution, which
enhances entanglement, and measurements which diminish it. In the thermodynamic
limit, there is a phase transition from volume law entanglement to area law
entanglement at a critical value of measurement frequency. This phenomenon,
occurring in hybrid quantum circuits with both unitary gates and measurements,
is termed as measurement-induced phase transition (MIPT). We study the behavior
of MIPT in circuits comprising of two qubit unitary gates parameterized by
Cartan decomposition. We show that the entangling power and gate typicality of
the two-qubit local unitaries employed in the circuit can be used to explain
the behavior of global bipartite entanglement the circuit can sustain. When the
two qubit gate throughout the circuit is the identity and measurements are the
sole driver of the entanglement behavior, we obtain analytical estimate for the
entanglement entropy that shows remarkable agreement with numerical
simulations. We also find that the entangling power and gate typicality enable
the classification of the two-qubit unitaries by different universality classes
of phase transitions that can occur in the hybrid circuit. For all unitaries in
a particular universality class, the transition from volume to area law of
entanglement occurs with same exponent that characterizes the phase transition.
