Continuous weak measurement of a qubit on the Bloch sphere. Quantum Zeno effect, measurement-induced phase transitions, and the interplay between unitary evolution and projective collapse.
Quantum Zeno effect: frequent measurement freezes evolution. Lindblad master equation: dρ/dt = -i[H,ρ] + Γ(σ_z ρ σ_z - ρ). Continuous measurement: quantum trajectory = stochastic Schrödinger eq, Wiener noise drives state towards eigenstates. Measurement-induced phase transition (MIPT): in many-body circuits with rate p, entanglement goes from volume law (p→0) to area law (p→1) at p_c (Li-Fisher 2018).