On some special cases of the Entropy Photon-Number Inequality

TL;DR

This paper proves the Entropy Photon-Number Inequality (EPnI) in specific cases involving vacuum and certain high-entropy states, advancing understanding of quantum entropy inequalities.

Contribution

It establishes the validity of EPnI for particular classes of quantum states, including vacuum and states with specific eigenvalue structures.

Findings

EPnI holds when one input is vacuum and the other has eigenvectors as number states.

EPnI is valid for states with only two non-zero eigenvalues.

EPnI applies to high entropy states with arbitrary non-zero eigenvalues.

Abstract

We show that the Entropy Photon-Number Inequality (EPnI) holds where one of the input states is the vacuum state and for several candidates of the other input state that includes the cases when the state has the eigenvectors as the number states and either has only two non-zero eigenvalues or has arbitrary number of non-zero eigenvalues but is a high entropy state. We also discuss the conditions, which if satisfied, would lead to an extension of these results.