Quantum communication over finite bandwidth with time-limited signals

Most communication systems support frequency multiplexing over a finite bandwidth which can be characterized by their transmission spectra. Realistic quantum signals in quantum communication systems like transducers are inherently limited in time due to internal losses and channel instability, inhibiting the frequency multiplexing encoding. We calculate quantum channel capacities for pure-loss finite bandwidth and time-limited channels to establish the optimal communication strategy in a realistic setting. We derive analytical solutions of the optimal encoding and decoding modes for Lorentzian and box transmission spectra, along with numerical solutions for various other transmissions. Our findings reveal a general feature of sequential activation of quantum channels as the input signal duration increases, as well as the existence of optimal signal length for scenarios where only a limited number of channels are in use.