Resource distillation in convex Gaussian resource theories

TL;DR

This paper extends Gaussian resource theories to include convex mixtures, enabling limited resource distillation, and provides bounds and protocols for squeezing and entanglement distillation.

Contribution

It introduces convex Gaussian resource theories, demonstrating that resource distillation becomes possible with classical randomness, and establishes tight bounds with example protocols.

Findings

Resource distillation is possible in convex Gaussian theories.

Derived tight bounds for distillation limits.

Presented protocols for squeezing and entanglement distillation.

Abstract

It is known that distillation in continuous variable resource theories is impossible when restricted to Gaussian states and operations. To overcome this limitation, we enlarge the theories to include convex mixtures of Gaussian states and operations. This extension is operationally well-motivated since classical randomness is easily accessible. We find that resource distillation becomes possible for convex Gaussian resource theories-albeit in a limited fashion. We derive this limitation by studying the convex roof extension of a Gaussian resource measure and then go on to show that our bound is tight by means of example protocols for the distillation of squeezing and entanglement.