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

Doubly-parametric quantum transducers (DPTs), such as electro-opto-mechanical devices, show promise as quantum interconnects between the optical and microwave domains, thereby enabling long distance quantum networks between superconducting qubit systems. However, any transducer will inevitably introduce loss and noise that will degrade the performance of a quantum network. We explore how DPTs can be used to construct a network capable of distributing remote two-mode microwave entanglement over an optical link by comparing fourteen different network topologies. The fourteen topologies we analyze consist of combinations of different transducer operations, entangled resources, and entanglement swapping measurements. For each topology, we derive a necessary and sufficient analytic threshold on DPT parameters that must be exceeded in order to distribute microwave-microwave entanglement. We find that the thresholds are dependent on the given network topology, along with the available entanglement resources and measurement capabilities. In the high optical loss limit, which is relevant to realistic networks, we find that down-conversion of each half of an optical two-mode squeezed vacuum state is the most robust topology. Finally, we numerically evaluate the amount of microwave--microwave entanglement generated for each topology using currently achievable values for DPT parameters, entangled resources, and swapping measurements, finding the encouraging result that several topologies are within reach of current experimental capabilities.