  Feedback control engineers have been interested in MIMO (multiple-input
multiple-output) extensions of SISO (single-input single-output) results of
various kinds due to its rich mathematical structure and practical
applications. An outstanding problem in quantum feedback control is the
extension of the SISO theory of Markovian feedback by Wiseman and Milburn
[Phys. Rev. Lett. {\bf 70}, 548 (1993)] to multiple inputs and multiple
outputs. Here we generalize the SISO homodyne-mediated feedback theory to allow
for multiple inputs, multiple outputs, and \emph{arbitrary} diffusive quantum
measurements. We thus obtain a MIMO framework which resembles the SISO theory
and whose additional mathematical structure is highlighted by the extensive use
of vector-operator algebra.

Quantum Physics