Bilinear Hamiltonian interactions between linear quantum systems via feedback

A number of recent works employ bilinear Hamiltonian interactions between Linear Quantum Stochastic Systems (LQSSs). To the authors' knowledge, implementation schemes for such interactions exist only between single-mode systems. In this work, we propose a general method for the implementation of an arbitrary bilinear Hamiltonian interaction between two multi-mode LQSSs via a feedback interconnection. As an application, we show that the direct interaction realization of a certain coherent quantum control architecture is very useful for design and optimization.