Universal Limit on Communication

TL;DR

This paper establishes a universal upper limit on the capacity of any communication channel based on energy and time, independent of system size or signal nature, with implications for quantum and classical signals.

Contribution

It derives a fundamental, system-size-independent bound on channel capacity based on energy and time, applicable to all quantum and classical communication systems.

Findings

The capacity is limited by the energy-time product, E Δt / ħ.

Quantum effects influence large message encoding even with classical signals.

The bound holds regardless of system size, mass, or signal processing methods.

Abstract

I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order $E \Delta t / \hbar$, where $E$ is the average energy of the signal, and $\Delta t$ is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed. As an example, I consider the encoding of information in the transverse or angular position of a signal emitted and received by systems of arbitrarily large cross-section. In the limit of a large message space, quantum effects become important even if individual signals are classical, and the bound is upheld.