No-activation theorem for Gaussian nonclassical correlations by Gaussian operations

TL;DR

This paper demonstrates that Gaussian operations cannot activate nonclassical correlations into entanglement in Gaussian states, but non-Gaussian protocols can achieve this activation, providing insights into quantum correlations in continuous variable systems.

Contribution

It proves the no-activation theorem for Gaussian operations and constructs a non-Gaussian activation protocol for continuous variable Gaussian states.

Findings

Gaussian operations cannot generate entanglement from nonclassical Gaussian states.

A non-Gaussian activation protocol successfully activates nonclassical correlations.

Calculated negativity of quantumness for two-mode Gaussian states.

Abstract

We study general quantum correlations of continuous variable Gaussian states and their interplay with entanglement. Specifically, we investigate the existence of a quantum protocol activating all nonclassical correlations between the subsystems of an input bipartite continuous variable system, into output entanglement between the system and a set of ancillae. For input Gaussian states, we prove that such an activation protocol cannot be accomplished with Gaussian operations, as the latter are unable to create any output entanglement from an initial separable yet nonclassical state in a worst-case scenario. We then construct a faithful non-Gaussian activation protocol, encompassing infinite-dimensional generalizations of controlled-NOT gates to generate entanglement between system and ancillae, in direct analogy with the finite-dimensional case. We finally calculate the negativity of quantumness, an operational measure of nonclassical correlations defined in terms of the performance of the activation protocol, for relevant classes of two-mode Gaussian states.