Restricted Monte Carlo wave-function method and Lindblad equation for identifying entangling open-quantum-system dynamics

We develop an extension of the Monte Carlo wave function approach that unambiguously identifies dynamical entanglement in general composite, open systems. Our algorithm performs tangential projections onto the set of separable states, leading to classically correlated quantum trajectories. By comparing this restricted evolution with the unrestricted one, we can characterize the entangling capabilities of quantum channels without making use of input-output relations. Moreover, applying this method is equivalent to solving the nonlinear master equation in Lindblad form introduced in \cite{PAH24} for two-qubit systems. We here extend these equations to multipartite systems of qudits, describing non-entangling dynamics in terms of a stochastic differential equation. We identify the impact of dynamical entanglement in open systems by applying our approach to several correlated decay processes. Therefore, our methodology provides a complete and ready-to-use framework to characterize dynamical quantum correlations caused by arbitrary open-system processes.