Quantum-trajectory unravelling

A quantum-trajectory unravelling represents a Lindblad equation as an ensemble of stochastic pure-state histories. Between jumps a state evolves under the non-Hermitian effective Hamiltonian $H_{\mathrm{eff}}=H-\frac{i}{2}{\sum }_{\alpha }{L}_{\alpha }^{†}{L}_{\alpha }$, while a jump of type $\alpha$ sends it to a normalized multiple of $L_{\alpha }|\psi ⟩$.

A pure stationary state is dark when every jump operator acts on it as a scalar, after an allowed shift of the jump operators, and the corresponding effective Hamiltonian preserves its ray. Every trajectory that reaches such a state remains on that same ray.