Exact Finite-Dimensional Evaluation of Homodyne Quantum Trajectories for Single-Quadrature Hamiltonian

• URL: http://arxiv.org/abs/2607.26093v1
• Date: Tue, 28 Jul 2026 00:32:22 GMT
• Title: Exact Finite-Dimensional Evaluation of Homodyne Quantum Trajectories for Single-Quadrature Hamiltonian
• Abstract summary: We identify an exactly solvable class of continuously monitored systems.<n>We derive an exact finite-angle representation of the conditional dynamics for arbitrary finite-order quadrature moments.<n>The resulting equations depend only on the Hamiltonian degree and moment order, with computational complexity independent of the Hilbert-space dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 moment order, with computational complexity $\mathcal{O}(C_{d,n}T)$, independent of the Hilbert-space dimension. The method requires no Fock-space truncation, Gaussian approximation, or moment closure approximation. Numerical simulations demonstrate agreement with direct stochastic master equation evolution and establish an efficient exact method for studying nonlinear homodyne trajectories in this class of continuously monitored systems.

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