  High-performance quantum transducers, which can faithfully convert quantum
information between disparate physical carriers, are essential elements in
quantum science and technology. To assess their ability to coherently transfer
quantum information, quantum transducers are typically characterized by
different figures of merit including conversion efficiency, bandwidth, and
added noise. Here we utilize the concept of quantum capacity, the highest
achievable qubit communication rate through a channel, to quantify the
performance of a transducer. By evaluating the continuous-time quantum capacity
across the conversion band, quantum capacity can serve as a single metric that
unifies various desirable criteria of a transducer -- high efficiency, large
bandwidth, and low noise. Moreover, using the quantum capacities of bosonic
pure-loss channels as benchmarks, we investigate the optimal designs of generic
quantum transduction schemes implemented by transmitting external signals
through a coupled bosonic chain. Under the physical constraint of a bounded
maximal coupling rate $g_{\rm max}$, the highest continuous-time quantum
capacity $Q^{\rm max} \approx 31.4 g_{\rm max}$ is achieved by transducers with
a maximally flat conversion frequency response, analogous to Butterworth
electric filters. We further extend our method to include thermal noise by
considering upper and lower bounds on the quantum capacities of transducers and
characterize the performance of maximally flat transducers under the effect of
thermal loss.
