Separability Criterion for One-Sided Gaussian Channels

TL;DR

This paper establishes a criterion to determine whether a one-sided Gaussian quantum channel preserves or destroys entanglement in pure Gaussian states, showing that the outcome depends solely on the channel, not the input state.

Contribution

It introduces a linear-algebraic separability criterion for one-sided Gaussian channels, providing a simple method to assess entanglement preservation or destruction.

Findings

All output states are either entangled or separable for a fixed channel.

Entanglement preservation depends only on the channel, not the input state.

A simple criterion determines if a channel destroys entanglement.

Abstract

We show that the following nontrivial necessary precondition for an entanglement evolution equation for pure Gaussian states under one-sided Gaussian channels holds. Suppose a Gaussian quantum channel acts on one mode of a pure entangled multi-mode Gaussian input state. Then, for a fixed channel, either all output states are entangled or none of them are. In other words, if the input state is Gaussian, pure and entangled, the separability after a one-sided Gaussian quantum channel does not depend on the input state, but only on the channel. Furthermore, a simple linear-algebraic separability criterion allows to decide whether a given channel destroys the entanglement of pure entangled input states or leaves them entangled.