It takes half the energy of a photon to send one bit reliably on the Poisson channel with feedback

TL;DR

This paper demonstrates that reliably transmitting a single bit over a Poisson channel with feedback requires only half the energy of a photon, regardless of dark current, and extends the analysis to multiple bits.

Contribution

It provides a precise energy requirement for reliable communication over Poisson channels with feedback, including the case of multiple bits, revealing fundamental energy limits.

Findings

Sending one bit reliably requires half the energy of a photon.

The result holds regardless of dark current intensity.

The energy needed for multiple bits is also characterized.

Abstract

We consider the transmission of a single bit over the continuous-time Poisson channel with noiseless feedback. We show that to send the bit reliably requires, on the average, half the energy of a photon. In the absence of peak-power constraints this holds irrespective of the intensity of the dark current. We also solve for the energy required to send $log_{2} M$ bits.