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.

arXiv comment8+6 pages, 1 figure. Close to published version

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• Stellar representation of non-Gaussian quantum states
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• 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
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• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Gaussian Thermal Operations and the Limits of Algorithmic Cooling
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• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
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• 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
• Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems
• Bosonic quantum communication across arbitrarily high loss channels
• Faithful measure of Quantum non-Gaussianity via quantum relative entropy
• Assisted concentration of Gaussian resources
• A geometric measure of non-classicality
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
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• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
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• Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
• Unbreakable and breakable quantum censorship
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Exploring the possibility of a complex-valued non-Gaussianity measure for quantum states of light
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• Analyzing the free states of one quantum resource theory as resource states of another
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• Interpolated Collision Model Formalism
• Adaptive Non-Gaussian Quantum State Engineering
• Generating random Gaussian states
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• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Charge-Preserving Operations in Quantum Batteries
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• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
• Quantifying coherence of quantum measurements
• Information geometry of bosonic Gaussian thermal states
• Position representation of single-mode Gaussian channels beyond the Gaussian functional form
• Divisibility classes of qubit maps and singular Gaussian channels