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.

arXiv comment10+5 pages, 7 figures

References in corpus (37)

• Quantum entanglement
• Gaussian Quantum Information
• Concentrating Partial Entanglement by Local Operations
• Encoding a qubit in an oscillator
• Continuous variable quantum cryptography using coherent states
• Quantum key distribution using gaussian-modulated coherent states
• Quantum Resource Theories
• Quantum computation over continuous variables
• Teleportation of Quantum States
• Universal Quantum Computation with Continuous-Variable Cluster States
• Fundamental limitations for quantum and nano thermodynamics
• The second laws of quantum thermodynamics
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• The Resource Theory of Stabilizer Computation
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Gaussian transformations and distillation of entangled Gaussian states
• Quantum Distribution of Gaussian Keys with Squeezed States
• The general structure of quantum resource theories
• Hudson's Theorem for finite-dimensional quantum systems
• A No-Go Theorem for Gaussian Quantum Error Correction
• Driving non-Gaussian to Gaussian states with linear optics
• Convex resource theory of non-Gaussianity
• Gaussian Entanglement of Formation
• Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting
• Gaussian quantum resource theories
• Distillation of continuous-variable entanglement with optical means
• Limitations of quantum computing with Gaussian cluster states
• Encoding an oscillator into many oscillators
• Experimental demonstration of continuous variable purification of squeezed states
• Experimental distillation of squeezing from non-Gaussian quantum states
• Entanglement generation and Hamiltonian simulation in Continuous-Variable Systems
• Quantification and manipulation of magic states
• The first law of general quantum resource theories
• Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator
• Information and noise in quantum measurement

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