Communication and energy

The quantum limitations on the maximum communication rate (capacity) possible through a single noiseless channel with signals of finite duration are investigated. They may be summarized in the characteristic information function defined here. In the absence of dispersion this description is a Lorentz-invariant one, and applies also in the presence of exterior gravitational fields. For long duration the characteristic information function corresponds to the standard quantum-channel-capacity formula of Gordon, of Lebedev and Levitin, and of Pendry. For finite signal duration it proves useful to distinguish between heralded and self-heralding signals, according to whether their arrival is anticipated or not. The two types have different characteristic functions. These are calculated here for occupation-number signal states in channels where the carrier quantum field may be represented by independent modes. The Gordon-Lebedev-Levitin-Pendry formula provides an upper bound to the exact results for both types of signals. The linear bound on communication rate of Bremermann and the present author bounds the capacity only for self-heralding signals. However, it is the better estimator of capacity for self-heralding signals with modest information content.