Quantum Limitations on the Storage and Transmission of Information

Abstract

Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady state and burst communication. An analytic approximation is given for the maximum signal information possible with occupation number signal states as a function of mean signal energy. A theorem guaranteeing that these states are optimal for communication is proved. A heuristic "proof" of the linear bound on communication is given, followed by rigorous proofs for signals with specified mean energy, and for signals with given energy budget. And systems of many parallel quantum channels are shown to obey the linear bound for a natural channel architecture. The time-energy uncertainty principle is reformulated in information language by means of the linear bound. The quantum bound on information storage capacity of quantum mechanical and quantum field devices is reviewed. A simplified version of the analytic proof for the bound is given for the latter case. Solitons as information caches are discussed, as is information storage in one dimensional systems. The influence of signal self-gravitation on communication is considerd. Finally, it is shown that acceleration of a receiver acts to block information transfer.

Black holes and information theory

“…Being a statement about entropy of a system, the universal bound can also be derived directly from statistical mechanics for simple (quantum) systems [49,50]. None of these analytical or numerical arguments have the simplicity or broad applicability of the argument described above.…”

“…Let us consider the limit λ c → ∞. The capacity of such a cutoff-free channel is known [50,57]. Regardless of the dispersion relation obeyed by the waveṡ…”

Heat Transfer in Black Holes

“…The solution obtained for the postulated metric give a place to imaginary numbers that allow glimpsing material with quantized energy. The theorem "a black hole has no hair" [14][15][16][17][18][19][20][21], concludes that the behavior of the gigantic mass compressed to a black hole with the mass of a mountain, is conceived by the quantum mechanics like a microscopic radius particle smaller than the radius of a neutron or a proton, which allows to demonstrate an intrinsic bond between General Relativity and the Quantum Theory through the Quantum Gravity. …”

Will ET write or radiate: inscribed matter vs. electromagnetic channels

“…Absolute bounds on mass information density have been described in [22], but these limits assume matter in its densest possible state (a black hole) and are far larger than what can be obtained practically with ordinary matter. In contrast, clear limits on the maximum possible information storage density for ordinary inscribed matter are unknown.…”

“…In FIGURE 2 we provide iso-Ω contours as a function of D and A for communications with δ ¥ 10 3 (v about 7 times larger than solar escape velocity at earth distance) andρ ¥ 10 22 . Points corresponding to examples of receiver apertures and wavelengths at various distances are as shown.…”