# The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier

## TL;DR

This paper calculates the maximum squashed entanglement for noiseless quantum Gaussian channels and introduces the first lower bound for such entanglement in Gaussian states, advancing understanding of quantum channel capacities.

## Contribution

It provides the first lower bound on the squashed entanglement of quantum Gaussian states and channels, and compares classical and quantum squashed entanglement for these states.

## Key findings

- Maximum squashed entanglement achieved with infinitely squeezed two-mode vacuum states.
- First lower bound established for the squashed entanglement of Gaussian states.
- Classical squashed entanglement exceeds quantum squashed entanglement for the studied states.

## Abstract

We determine the maximum squashed entanglement achievable between sender and receiver of the noiseless quantum Gaussian attenuators and amplifiers and we prove that it is achieved sending half of an infinitely squeezed two-mode vacuum state. The key ingredient of the proof is a lower bound to the squashed entanglement of the quantum Gaussian states obtained applying a two-mode squeezing operation to a quantum thermal Gaussian state tensored with the vacuum state. This is the first lower bound to the squashed entanglement of a quantum Gaussian state and opens the way to determine the squashed entanglement of all quantum Gaussian channels. Moreover, we determine the classical squashed entanglement of the quantum Gaussian states above and show that it is strictly larger than their squashed entanglement. This is the first time that the classical squashed entanglement of a mixed quantum Gaussian state is determined.