Exact Finite-Dimensional Evaluation of Homodyne Quantum Trajectories for Single-Quadrature Hamiltonian
Source: Originally published on arXiv quant-ph on July 30, 2026.
arXiv:2607.26093v1 Announce Type: new Abstract: Simulation of nonlinear stochastic master equations generally requires trajectory-level evolution of large Hilbert-space density matrices, making strongly nonlinear continuously monitored systems computationally challenging. Here we identify an exactly solvable class of continuously monitored systems consisting of polynomial single-quadrature Hamiltonians, linear damping, and homodyne measurement of the same quadrature. For Gaussian initial states, we derive an exact finite-dimensional stochastic representation of the conditional dynamics for arbitrary finite-order quadrature moments $\langle Q^mP^n\rangle$ through closure of the conditional momentum hierarchy. The resulting coefficient equations depend only on the Hamiltonian degree and mome...
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