# Activation and superactivation of single-mode Gaussian quantum channels

## TL;DR

This paper explores activation and superactivation phenomena in single-mode Gaussian quantum channels, showing that superactivation can occur in many thermal attenuators, enabling quantum communication through highly noisy channels, while it does not occur in entanglement-breaking channels.

## Contribution

It provides a comprehensive analysis of activation and superactivation in all single-mode phase-insensitive Gaussian channels, identifying conditions under which superactivation occurs or is impossible.

## Key findings

- Superactivation occurs in a broad range of thermal attenuator channels.
- Activation phenomena are more common than previously thought.
- Superactivation is impossible in entanglement-breaking Gaussian channels with finite energy.

## Abstract

Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low. This means that we can transmit quantum information reliably through very noisy Gaussian channels having zero quantum capacity. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the non-activation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.