Error bounds on finite-dimensional approximations of input-output open quantum systems

Many physical systems of interest that are encountered in practice are input-output open quantum systems described by quantum stochastic differential equations and defined on an infinite-dimensional underlying Hilbert space. Most commonly, these systems involve coupling to a quantum harmonic oscillator as a system component. This paper is concerned with the error in the finite-dimensional approximation of input-output open quantum systems defined on an infinite-dimensional underlying Hilbert space. We present explicit error bounds between the time evolution of the state of a class of infinite-dimensional quantum systems and its approximation on a finite-dimensional subspace of the original, when both are initialized in the latter subspace. Application to a physical example drawn from the literature is provided to illustrate our results.