The general structure of quantum resource theories

Abstract

In recent years it was recognized that properties of physical systems such as entanglement, athermality, and asymmetry, can be viewed as resources for important tasks in quantum information, thermodynamics, and other areas of physics. This recognition followed by the development of specific quantum resource theories (QRTs), such as entanglement theory, determining how quantum states that cannot be prepared under certain restrictions may be manipulated and used to circumvent the restrictions. Here we discuss the general structure of QRTs, and show that under a few assumptions (such as convexity of the set of free states), a QRT is asymptotically reversible if its set of allowed operations is maximal; that is, if the allowed operations are the set of all operations that do not generate (asymptotically) a resource. In this case, the asymptotic conversion rate is given in terms of the regularized relative entropy of a resource which is the unique measure/quantifier of the resource in the asymptotic limit of many copies of the state. This measure also equals the smoothed version of the logarithmic robustness of the resource.

5 pages, no figures, few references added, published version

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• Many-body quantum magic
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• Operational Advantage of Quantum Resources in Subchannel Discrimination
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• Quantifying the Imaginarity of Quantum Mechanics
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• Operational Resource Theory of Quantum Channels
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• Quantifying magic for multi-qubit operations
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• Convex geometry of quantum resource quantification
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• Resource Theory of Coherence - Beyond States
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• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Certification and Quantification of Multilevel Quantum Coherence
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• Harvesting Entanglement with Detectors Freely Falling into a Black Hole
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• Application of the Resource Theory of Channels to Communication Scenarios
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• Deterministic Coherence Distillation
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• Quantum Relative Lorenz Curves
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• Journeys from Quantum Optics to Quantum Technology
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• Fundamental Limits on Correlated Catalytic State Transformations
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• Discordlike correlation of bipartite coherence
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• Dephasing-Covariant Operations Enable Asymptotic Reversibility of Quantum Resources
• One-Shot Manipulation of Dynamical Quantum Resources
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• Tight constraints on probabilistic convertibility of quantum states
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• Approximate reversal of quantum Gaussian dynamics
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• Extracting Quantum Dynamical Resources: Consumption of Non-Markovianity for Noise Reduction
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• Resource theory of quantum thermodynamics: Thermal operations and Second Laws
• The operational significance of the quantum resource theory of Buscemi nonlocality
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• Unified framework for quantumness -- coherence, discord, and entanglement
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
• Quantifying dynamical coherence with coherence measures
• Unification of quantum resources in distributed scenarios
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• Converting coherence based on positive-operator-valued measures into entanglement
• Quantum Bell Nonlocality is Entanglement
• What it takes to shun equilibration
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Simple Bounds for One-shot Pure-State Distillation in General Resource Theories
• Universal resources for quantum computing
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
• Dynamics of incompatibility of quantum measurements in open systems
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• Geometric-Like imaginarity: quantification and state conversion
• Measuring non-Markovianity via incoherent mixing with Markovian dynamics
• Minimum Stabilizing Energy Release for Mixing Processes
• Quantum Resource Control for noisy EPR-steering with qubit measurements
• Accessible bounds for general quantum resources
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• Compositional resource theories of coherence
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• Quantum Causal Structure and Quantum Thermodynamics
• Probabilistic state synthesis based on optimal convex approximation
• Coherence filtration under strictly incoherent operations
• Upper and Lower Bounds on Phase-Space Rearrangements
• The Zero-error Entanglement Cost is Highly Non-Additive
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• Classically Replaceable Operations
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• Complementary Resource Relation of Concurrence and Roughness for atwo Qubits State
• Smooth entropy in axiomatic thermodynamics
• The optimal approximation of qubit states with limited quantum states
• Non-Conformal Behavior of Holographic Entanglement Measures
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Continuity of the relative entropy of resource
• Thermal coherence of the Heisenberg model with Dzyaloshinsky-Moriya interactions in an inhomogenous external field
• Unifying Entanglement with Uncertainty via Symmetries of Observable Algebras
• Probabilistic unitary synthesis with optimal accuracy
• Covariant influences for finite discrete dynamical systems
• One-shot manipulation of coherence in dynamic quantum resource theory
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
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• Asymptotic quantification of entanglement with a single copy
• Resource distillation in convex Gaussian resource theories
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• Operational Resource Theory of Non-Markovianity
• Breaking global symmetries with locality-preserving operations
• Operational approach to the topological structure of the physical space
• Analytically Computable Symmetric Quantum Correlations
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• Strong superadditivity relations for multiqubit systems
• The best approximation of a given qubit state with the limited pure-state set
• Extending Resource Monotones using Kan Extensions
• Exposure of subtle multipartite quantum nonlocality
• Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
• Symmetric channel verification for purifying noisy quantum channels
• A Bayesian view of Single-Qubit Clocks, and an Energy versus Accuracy tradeoff
• Minimizing Quantum Renyi Divergences via Mirror Descent with Polyak Step Size
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• Environment engineering to protect quantum coherence in tripartite systems under dephasing noise
• Quantum coherence measures for generalized Gaussian wave packets under a Lorentz boost
• Strong bounds on required resources for quantum channels by local operations and classical communication
• Methods of constructing superposition measures
• Thermodynamic criteria for signaling in quantum channels
• Detecting Non-Markovianity via Quantified Coherence: Theory and Experiments
• Entropic and operational characterizations of dynamic quantum resources
• Monotonicity Under Local Operations: Linear Entropic Formulas
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Simplest non-additive measures of quantum resources
• Mathematical methods for resource-based type theories
• The reduction of the number of incoherent Kraus operations for qutrit systems
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• The coherent measurement cost of coherence distillation