Standard super-activation for Gaussian channels requires squeezing

TL;DR

This paper proves that squeezing is essential for super-activation of quantum capacity in Gaussian channels, demonstrating that without squeezing, channels cannot exhibit this phenomenon, thus confirming a key conjecture.

Contribution

The paper proves that squeezing is necessary for super-activation in Gaussian channels and provides a counterexample showing the limitation of positive partial transpose criteria.

Findings

Squeezing is required for super-activation of Gaussian channels.

Gauge covariant channels with positive partial transpose are entanglement-breaking.

Counterexample shows the failure of the implication for channels from passive interactions with squeezed environments.

Abstract

The quantum capacity of bosonic Gaussian quantum channels can be non-additive in a particularly striking way: a pair of such optical-fiber type channels can individually have zero quantum capacity but super-activate each other such that the combined channel has strictly positive capacity. This has been shown in [Nature Photonics 5, 624 (2011)] where it was conjectured that squeezing is a necessary resource for this phenomenon. We provide a proof of this conjecture by showing that for gauge covariant channels a Choi matrix with positive partial transpose implies that the channel is entanglement-breaking. In addition, we construct an example which shows that this implication fails to hold for Gaussian channels which arise from passive interactions with a squeezed environment.