  This paper aims to provide conditions under which a quantum stochastic
differential equation can serve as a model for interconnection of a bilinear
system evolving on an operator group SU(2) and a linear quantum system
representing a quantum harmonic oscillator. To answer this question we derive
algebraic conditions for the preservation of canonical commutation relations
(CCRs) of quantum stochastic differential equations (QSDE) having a subset of
system variables satisfying the harmonic oscillator CCRs, and the remaining
variables obeying the CCRs of SU(2). Then, it is shown that from the physical
realizability point of view such QSDEs correspond to bilinear-linear quantum
cascades.
