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Doubly-parametric quantum transducers (DPTs), such as electro-opto-mechanicaldevices, show promise as quantum interconnects between the optical andmicrowave domains, thereby enabling long distance quantum networks betweensuperconducting qubit systems. However, any transducer will inevitablyintroduce loss and noise that will degrade the performance of a quantumnetwork. We explore how DPTs can be used to construct a network capable ofdistributing remote two-mode microwave entanglement over an optical link bycomparing fourteen different network topologies. The fourteen topologies weanalyze consist of combinations of different transducer operations, entangledresources, and entanglement swapping measurements. For each topology, we derivea necessary and sufficient analytic threshold on DPT parameters that must beexceeded in order to distribute microwave-microwave entanglement. We find thatthe thresholds are dependent on the given network topology, along with theavailable entanglement resources and measurement capabilities. In the highoptical loss limit, which is relevant to realistic networks, we find thatdown-conversion of each half of an optical two-mode squeezed vacuum state isthe most robust topology. Finally, we numerically evaluate the amount ofmicrowave--microwave entanglement generated for each topology using currentlyachievable values for DPT parameters, entangled resources, and swappingmeasurements, finding the encouraging result that several topologies are withinreach of current experimental capabilities.

Optically Distributing Remote Two-node Microwave Entanglement using Doubly Parametric Quantum Transducers