Optimization and Comparison of Two-node Gaussian Quantum Networks with Optical-Microwave Transducers

Achieving quantum communication between two remote microwave nodes connected via an optical link will require quantum transducers, many of which can be modeled as two-mode Gaussian quantum channels between optical and microwave modes. We propose a method for finding the optimal network for distributing microwave-microwave entanglement under certain restrictions, such allowing only Gaussian resources in the optical domain. We show that networks which utilize the two-mode nature of the transducer via ancillary states/measurements outperform those where the transducer is reduced to an effective single mode operation (e.g. upconversion). We are then able to upper-bound the achievable microwave-microwave entanglement rates for experimentally relevant transducers, such as electro-opto-mechanical devices.