In this paper, we give two independent and rigorous derivations for the quantum bound on the information transmission rate proposed independently by Bekenstein [Phys. Rev. Lett. 46, 623 (1981)] and Bremermann. ul2 [Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, edited by L. M. LeCam and J. Neyman (University of California Press, Berkeley, 1967], preceded by a heuristic argument showing why such a bound must hold. In both approaches, information carriers are quanta for some field. The first method resembles the microcanonical approach to statistical mechanics, where the strategy of overestimating the real number of states by relaxing the indistinguishability of quanta was adopted. The second is based entirely upon maximum-entropy methods. Amazingly enough, the results obtained by these physically unrelated premises turn out to be identical, namely, that the single (noiseless) channel capacity is Imax=E/2Latin small letter h with stroke bits s-1. It is further shown that, in a finite time , no information can ever be conveyed unless the energy threshold 2Latin small letter h with stroke/ is reached, allowing the reinterpretation of the time-energy uncertainty in informational-theoretic language.