Gaussian quantum resource theories

Abstract

We develop a general framework to assess capabilities and limitations of the Gaussian toolbox in continuous variable quantum information theory. Our framework allows us to characterize the structure and properties of quantum resource theories specialized to Gaussian states and Gaussian operations, establishing rigorous methods for their description and yielding a unified approach to their quantification. We show in particular that, under a few intuitive and physically motivated assumptions on the set of free states, no Gaussian quantum resource can be distilled with free Gaussian operations, even when an unlimited supply of the resource state is available. This places fundamental constraints on state manipulations in all such Gaussian resource theories. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A comprehensive semidefinite programming representation of all these resources is explicitly provided.

8+6 pages, 1 figure. Close to published version

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Cited by in corpus (70)

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• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
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• Stellar representation of non-Gaussian quantum states
• One-Shot Operational Quantum Resource Theory
• Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing
• Operational resource theory of continuous-variable nonclassicality
• Resource theory of non-Gaussian operations
• Nonclassical Light and Metrological Power: An Introductory Review
• Cost of quantum entanglement simplified
• Semidefinite programming relaxations for quantum correlations
• Skew informations from an operational view via resource theory of asymmetry
• Generic bound coherence under strictly incoherent operations
• Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis
• No-go theorems for quantum resource purification II: new approach and channel theory
• Non-asymptotic assisted distillation of quantum coherence
• Operational quantification of continuous-variable quantum resources
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Gaussian Thermal Operations and the Limits of Algorithmic Cooling
• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Quantum read-out for cold atomic quantum simulators
• Universal limitations on implementing resourceful unitary evolutions
• Communication, Dynamical Resource Theory, and Thermodynamics
• Resource theory of superposition: State transformations
• The Unruh effect in slow motion
• All phase-space linear bosonic channels are approximately Gaussian dilatable
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Bosonic quantum communication across arbitrarily high loss channels
• Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems
• Faithful measure of Quantum non-Gaussianity via quantum relative entropy
• Assisted concentration of Gaussian resources
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• One-shot manipulation of entanglement for quantum channels
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• A geometric measure of non-classicality
• Decoding Quantum Field Theory with Machine Learning
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• The non-stabilizerness of fermionic Gaussian states
• Catalytic Gaussian thermal operations
• Censorship of Quantum Resources in Quantum Networks
• Hierarchy of continuous-variable quantum resource theories
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Superdense Coding in Resource Theory of Asymmetry
• Unbreakable and breakable quantum censorship
• Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
• Resource distillation in convex Gaussian resource theories
• Exploring the possibility of a complex-valued non-Gaussianity measure for quantum states of light
• Fundamental limitations to key distillation from Gaussian states with Gaussian operations
• Projective robustness for quantum channels and measurements and their operational significance
• Thermodynamics of coupled time crystals with an application to energy storage
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Analyzing the free states of one quantum resource theory as resource states of another
• Interpolated Collision Model Formalism
• Continuous Variable Quantum Advantages and Applications in Quantum Optics
• Generating random Gaussian states
• Adaptive Non-Gaussian Quantum State Engineering
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
• Charge-Preserving Operations in Quantum Batteries
• Characterization of non-adaptive Clifford channels
• Entropic and operational characterizations of dynamic quantum resources
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Divisibility classes of qubit maps and singular Gaussian channels
• Position representation of single-mode Gaussian channels beyond the Gaussian functional form
• Information geometry of bosonic Gaussian thermal states
• Quantifying coherence of quantum measurements