Competition between unitary entanglement and measurement-induced collapse
In a monitored quantum circuit, random unitary gates grow entanglement (volume law: S ~ L), while local measurements collapse qubits and reduce entanglement (area law: S ~ const). A phase transition occurs at critical measurement rate p_c ≈ 0.16 (random Clifford). The entanglement entropy S follows S ~ log(L) at criticality (conformal field theory, c≈0.3). This transition has no classical analogue.