Invariant states of linear quantum stochastic systems under Weyl perturbations of the Hamiltonian and coupling operators
For researchers in quantum control and open quantum systems, this provides a perturbation framework to study non-Gaussian effects, though it is an incremental extension of existing Wigner-Moyal methods.
This paper analyzes how nonlinear Weyl perturbations of the Hamiltonian and coupling operators affect invariant states in linear quantum stochastic systems, deriving first-order corrections to the quasi-characteristic function for Hurwitz dynamics. The results enable approximate computation and analysis of non-Gaussian state generation in nonlinear quantum systems.
This paper is concerned with the sensitivity of invariant states in linear quantum stochastic systems with respect to nonlinear perturbations. The system variables are governed by a Markovian Hudson-Parthasarathy quantum stochastic differential equation (QSDE) driven by quantum Wiener processes of external bosonic fields in the vacuum state. The quadratic system Hamiltonian and the linear system-field coupling operators, corresponding to a nominal open quantum harmonic oscillator, are subject to perturbations represented in a Weyl quantization form. Assuming that the nominal linear QSDE has a Hurwitz dynamics matrix and using the Wigner-Moyal phase-space framework, we carry out an infinitesimal perturbation analysis of the quasi-characteristic function for the invariant quantum state of the nonlinear perturbed system. The resulting correction of the invariant states in the spatial frequency domain may find applications to their approximate computation, analysis of relaxation dynamics and non-Gaussian state generation in nonlinear quantum stochastic systems.