Princeton University Defines Limits of Accurate Quantum Filtering

Image: © 2006 The Trustees of Princeton University · princeton.edu The transfer operator KO maps alterations in historical measurement records to modifications in prospective conditional observables. For polynomial bosonic systems subject to continuous quadrature monitoring, this analysis reveals a distinct boundary delineating finite and infinite realizability. Gaussian dynamics and the Conditional Momentum Moment class enable precise finite-dimensional filters. Conversely, nonlinear dynamics falling outside these classifications typically generate an indefinite number of independent response directions and preclude key finite-dimensional C1 observable or state-level filtering. The singular values of KO subsequently broaden the realization framework to encompass approximation, yielding the optimal rank-d local-response error exceeding that achievable within those finite classes. Numerical experiments with Kerr and Duffing oscillators, together with a dynamics-adapted Poisson, Charlier construction for Kerr dynamics, show how this observable-level benchmark interacts…