Synthesis of linear quantum stochastic systems via quantum feedback networks

Recently, Nurdin, James and Doherty have demonstrated that an arbitrary linear quantum stochastic system can be realized as a cascade connection of simple one degree of freedom quantum harmonic oscillators together with a direct interaction Hamiltonian which is bilinear in the canonical operators of the oscillators. However, from an experimental point of view, direct interaction Hamiltonians are challenging to implement for systems with more than just a few degrees of freedom. In order to facilitate simpler experimental realizations of these systems, this paper develops a new synthesis algorithm for linear quantum stochastic systems that relies solely on field-mediated interactions, including in implementation of the direct interaction Hamiltonian. An explicit synthesis example is provided to illustrate the realization of a two degrees of freedom linear quantum stochastic system using the new algorithm.