One-Shot Operational Quantum Resource Theory

Abstract

A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-non-specific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation. We find general bounds on the optimal rates characterized by resource measures based on the smooth max/min-relative entropies and hypothesis testing relative entropy, as well as the free robustness measure, providing them with general operational meanings in terms of optimal state conversion. Our results encompass a wide class of resource theories via the theory-dependent coefficients we introduce, and the discussions are solidified by important examples, such as entanglement, coherence, superposition, magic states, asymmetry, and thermal non-equilibrium.

26 pages, 2 figures

References in corpus (71)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantifying Coherence
• Quantum Coherence as a Resource
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Resource Theories
• Conditions for a class of entanglement transformations
• Fundamental limitations for quantum and nano thermodynamics
• On quantum Renyi entropies: a new generalization and some properties
• The second laws of quantum thermodynamics
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Robustness of entanglement
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• The Resource Theory of Stabilizer Computation
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Application of a resource theory for magic states to fault-tolerant quantum computing
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• The asymptotic entanglement cost of preparing a quantum state
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• One-Shot Classical-Quantum Capacity and Hypothesis Testing
• A mathematical theory of resources
• (Quantumness in the context of) Resource Theories
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Quantifying Entanglement with Witness Operators
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Reversible transformations from pure to mixed states, and the unique measure of information
• Max- relative entropy of coherence: an operational coherence measure
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Convex resource theory of non-Gaussianity
• Maximal Coherence and the Resource Theory of Purity
• How robust is a quantum gate in the presence of noise?
• Genralized Robustness of Entanglement
• Quantifying Superposition
• The work value of information
• A resource theory of superposition
• Resource Destroying Maps
• Quantifying quantum resources with conic programming
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Comparison of Quantum Channels by Superchannels
• One-shot coherence distillation
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Gaussian quantum resource theories
• Efficiently computable bounds for magic state distillation
• Convex geometry of quantum resource quantification
• A resource theory of quantum memories and their faithful verification with minimal assumptions
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Beyond heat baths: Generalized resource theories for small-scale thermodynamics
• Operational relevance of resource theories of quantum measurements
• Certification and Quantification of Multilevel Quantum Coherence
• Quantum resource theories in the single-shot regime
• One-Shot Coherence Dilution
• Relative entropy is an exact measure of non-Gaussianity
• Quantifying resource in catalytic resource theory
• Resource convertibility and ordered commutative monoids
• Entanglement cost in practical scenarios
• Generalized Entropies
• Quantifying the resource content of quantum channels: An operational approach
• Beyond heat baths II: Framework for generalized thermodynamic resource theories
• A limit of the quantum Renyi divergence
• Resource theories of quantum channels and the universal role of resource erasure
• Microcanonical thermodynamics in general physical theories
• Resource theories of knowledge
• Some notes on the robustness of k-coherence and k-entanglement
• No energy transport without discord
• Diagonal quantum discord

Cited by in corpus (72)

• Many-body quantum magic
• Operational Resource Theory of Quantum Channels
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• No-Go Theorems for Quantum Resource Purification
• Application of the Resource Theory of Channels to Communication Scenarios
• Benchmarking one-shot distillation in general quantum resource theories
• Dynamical Entanglement
• Entanglement of a bipartite channel
• Fundamental limitations on distillation of quantum channel resources
• Resource theory of quantum scrambling
• Resource theory of asymmetric distinguishability
• Skew informations from an operational view via resource theory of asymmetry
• Quantifying the resource content of quantum channels: An operational approach
• Probabilistic transformations of quantum resources
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• No-go theorems for quantum resource purification II: new approach and channel theory
• Symmetry-protected sign problem and magic in quantum phases of matter
• Operational quantification of continuous-variable quantum resources
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• Tight constraints on probabilistic convertibility of quantum states
• One-shot entanglement distillation beyond local operations and classical communication
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Energy-Consumption Advantage of Quantum Computation
• Virtual quantum resource distillation
• Magic of quantum hypergraph states
• Universal limitations on implementing resourceful unitary evolutions
• Communication, Dynamical Resource Theory, and Thermodynamics
• Quantifying coherence in terms of the pure-state coherence
• Resource theory of superposition: State transformations
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• The operational advantages provided by non-classical teleportation
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Virtual quantum resource distillation: General framework and applications
• Quantifying imaginarity in terms of pure-state imaginarity
• Incompatibility as a resource for programmable quantum instruments
• The axiomatic and the operational approaches to resource theories of magic do not coincide
• Optimal probabilistic distillation of quantum coherence
• The operational significance of the quantum resource theory of Buscemi nonlocality
• One-shot manipulation of entanglement for quantum channels
• Experimental demonstration of one-shot coherence distillation: High-dimensional state conversions
• General state transitions with exact resource morphisms: a unified resource-theoretic approach
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
• Simple Bounds for One-shot Pure-State Distillation in General Resource Theories
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Tight bounds for antidistinguishability and circulant sets of pure quantum states
• Resource Marginal Problems
• Approximate distillation of quantum coherence
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Absolutely $k$-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States
• Maximal Magic for Two-qubit States
• Black Box Work Extraction and Composite Hypothesis Testing
• Criterion for a state to be distillable via stochastic incoherent operations
• An introductory review on resource theories of generalized nonclassical light
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• One-shot manipulation of coherence in dynamic quantum resource theory
• Projective robustness for quantum channels and measurements and their operational significance
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Thermodynamic optimization of quantum algorithms: On-the-go erasure of qubit registers
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Golden states in resource theory of superposition
• Thermodynamic criteria for signaling in quantum channels
• Entropic and operational characterizations of dynamic quantum resources
• Closed expressions for one-qubit states of convex roof coherence measures
• Tight relations and equivalences between smooth relative entropies
• Scalable protocol to coherence estimation from scarce data: Theory and experiment