  The implementation of optimal statistical inference protocols for
high-dimensional quantum systems is often computationally expensive. To avoid
the difficulties associated with optimal techniques, here I propose an
alternative approach to quantum estimation and detection based on Volterra
filters. Volterra filters have a clear hierarchy of computational complexities
and performances, depend only on finite-order correlation functions, and are
applicable to systems with no simple Markovian model. These features make
Volterra filters appealing alternatives to optimal nonlinear protocols for the
inference and control of complex quantum systems. Applications of the
first-order Volterra filter to continuous-time quantum filtering, the
derivation of a Heisenberg-picture uncertainty relation, quantum state
tomography, and qubit readout are discussed.
