Capacity of the Bosonic Wiretap Channel and the Entropy Photon-Number Inequality

TL;DR

This paper links the capacity of bosonic channels to a quantum entropy inequality, showing that proving the Entropy Photon-Number Inequality would confirm the classical and quantum capacities of these channels.

Contribution

It demonstrates that the second minimum output entropy conjecture suffices to establish the capacity of the bosonic wiretap channel and connects these conjectures to the Entropy Photon-Number Inequality.

Findings

Proves the sufficiency of the second entropy conjecture for channel capacity.

Shows that the entropy conjectures follow from the EPnI.

Highlights the importance of the EPnI in quantum information theory.

Abstract

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in turn would also prove the quantum capacity of the lossy bosonic channel. The preceding minimum output entropy conjectures are then shown to be simple consequences of an Entropy Photon-Number Inequality (EPnI), which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) form classical information theory.