# Characterizing the Gaussian coherence-breaking channel and its property with assistant entanglement inputs

## TL;DR

This paper characterizes Gaussian coherence-breaking channels, explores their properties with entanglement inputs, and proves the additivity of their Gaussian classical capacity when combined with other Gaussian channels.

## Contribution

It provides a comprehensive characterization of n-mode Gaussian coherence-breaking channels and establishes the additivity of their Gaussian classical capacity.

## Key findings

- Tensor product of a GCBC and any Gaussian channel yields product states.
- Inclusion relations among GCBCs, GPPTC, GEBC, and GCQC are established.
- Gaussian classical capacity is additive for tensor products of GCBCs and Gaussian channels.

## Abstract

In the paper, we give a characterization of arbitrary $n$-mode Gaussian coherence breaking channels (GCBCs) and show the tensor product of a GCBC and arbitrary a Gaussian channel maps all input states into product states. The inclusion relation among GCBCs, Gaussian positive partial transpose channels (GPPTC), entanglement breaking channels (GEBC) and Gaussian classical-quantum channels (GCQC) is displayed. Finally, we prove that Gaussian classical ($\chi$-) capacity for the tensor products of GCBCs and arbitrary Gaussian channels is additive.