Engineering arbitrary two-mode Gaussian control using a multi-mode coupler

Quantum transduction and bosonic quantum information processing both rely on the ability to precisely control interactions between desired modes of a multimode system. Previous studies have shown that single-mode control operations and interference may be used in conjunction to selectively decouple modes or swap any pair of modes, starting from any generic multimode bosonic coupler. In this work, we develop a similar interference-based scheme that can engineer arbitrary two-mode Gaussian unitary operations between desired modes of a multimode system. We present our results for a 3-mode toy model system (representing an opto-electro-mechanical coupler) and demonstrate how we can use decoupling to construct effective two-mode squeezers and beamsplitters by varying just a single control parameter. We further establish how this parametric dependence may be used to achieve squeezing-free operation of our protocol.