We present a stochastic path integral formalism for continuous quantum measurement that enables the analysis of rare events using action methods. By doubling the quantum state space to a canonical phase space, we can write the joint probability density function of measurement outcomes and quantum state trajectories as a phase space path integral. Extremizing this action produces the most likely paths with boundary conditions defined by preselected and postselected states as solutions to a set of ordinary differential equations. As an application, we analyze continuous qubit measurement in detail and examine the structure of a quantum jump in the Zeno measurement regime.
Chantasri, A., Dressel, J., Jordan, A.N., 2013. Action principle for continuous quantum measurement. Physical Review A 88, 042110. doi:10.1103/PhysRevA.88.042110
American Physical Society