  Two-way microwave-optical quantum transduction is an essential capability to
connect distant superconducting qubits via optical fiber, and to enable quantum
networking at a large scale. In Bl\'esin, Tian, Bhave, and Kippenberg's
article, ``Quantum coherent microwave-optical transduction using high overtone
bulk acoustic resonances" (Phys. Rev. A, 104, 052601 (2021)), they lay out a
quantum transduction system that accomplishes this by combining a piezoelectric
interaction to convert microwave photons to GHz-scale phonons, and an
optomechanical interaction to up-convert those phonons into telecom-band
photons using a pump laser set to an adjacent telecom-band tone. In this work,
we discuss these coupling interactions from first principles in order to
discover what device parameters matter most in determining the transduction
efficiency of this new platform, and to discuss strategies toward system
optimization for near-unity transduction efficiency, as well as how noise
impacts the transduction process.
  In addition, we address the post-transduction challenge of separating single
photons of the transduced light from a classically bright pump only a few GHz
away in frequency by proposing a novel optomechanical coupling mechanism using
phonon-photon four-wave mixing via stress-induced optical nonlinearity and its
thermodynamic connection to higher-orders of electrostriction. Where this
process drives transduction by consuming pairs instead of individual pump
photons, it will allow a clean separation of the transduced light from the
classically bright pump driving the transduction process.
