The Entropy Photon-Number Inequality and its Consequences

TL;DR

This paper introduces the Entropy Photon-Number Inequality, a quantum analog of the classical Entropy Power Inequality, which underpins capacity theorems for bosonic channels in quantum information theory.

Contribution

It demonstrates that key minimum output entropy conjectures follow from the proposed Entropy Photon-Number Inequality, advancing understanding of quantum channel capacities.

Findings

Establishes the Entropy Photon-Number Inequality as a fundamental consequence of quantum mechanics.

Shows that existing capacity theorems depend on this inequality.

Provides a new perspective linking classical and quantum information inequalities.

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, broadcast, and wiretap 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. Here we show that the preceding minimum output entropy conjectures are simple consequences of an Entropy Photon-Number Inequality, which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) from classical information theory.