# Conditional quantum entropy power inequality for $d$-level quantum systems

## TL;DR

This paper extends the quantum entropy power inequality to finite-dimensional systems, proving a conditional version using majorization and concavity, with implications for quantum channel capacity analysis.

## Contribution

It introduces a conditional quantum entropy power inequality for finite-dimensional systems using majorization and concavity techniques.

## Key findings

- Proves a conditional quantum entropy power inequality for finite-dimensional systems.
- Shows local measurements after partial swap do not affect majorization relations.
- Provides a tool for analyzing quantum channel capacities.

## Abstract

We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert, Datta, and Ozols [J. Math. Phys. 57, 052202 (2016)]. Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.