Resource distillation in convex Gaussian resource theories

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.

10+5 pages, 7 figures

References in corpus (6)

• Universal Quantum Computation with Continuous-Variable Cluster States
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• A No-Go Theorem for Gaussian Quantum Error Correction
• Experimental demonstration of continuous variable purification of squeezed states
• Experimental distillation of squeezing from non-Gaussian quantum states

Cited by in corpus (3)

• Operational quantification of continuous-variable quantum resources
• Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources