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

Physical Realizability Conditions for Mixed Bilinear-Linear Quantum Cascades with Pure Field Coupling