Quantum Capacities of Transducers

High-performance quantum transducers, devices that can faithfully convert quantum information between disparate frequency domains, are essential elements in quantum science and technology. To assess their ability to coherently transfer quantum information, quantum transducers are typically characterized by different figure of merits including conversion efficiency, bandwidth, and added noise. Here we utilize the concept of quantum capacity, the highest achievable qubit communication rate through a quantum channel, to quantify the performance of a transducer. By evaluating the full-band quantum capacity across the conversion bandwidth, we propose a single metric of a transducer that can unify various criteria --- high efficiency, large bandwidth, and low noise. Moreover, we investigate the optimal designs of general quantum transduction systems by using the quantum capacity of bosonic pure-loss channels as a benchmark. For general conversion that involves N intermediate modes, we find that the highest full-band quantum capacity is achieved when a transducer has a maximally flat conversion frequency response, which is a direct analog to a (N+2)th-order Butterworth electrical filter. Our method may be further extended to include intrinsic losses and thermal noises.