General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks

Abstract

We establish an operational characterization of general convex resource theories -- describing the resource content of not only states, but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs) -- in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory. Specifically, we introduce quantifiers of resourcefulness of states, measurements, and channels in any GPT based on the generalized robustness, and show that they exactly characterize the maximum advantage that a given resource provides over all free states, measurements, or channels in a class of state or channel discrimination tasks. In quantum mechanics, we show that the robustness of measurement can be alternatively understood as the maximal increase in one-shot accessible information when compared to free measurements. We furthermore endow the standard robustness of a state with an operational meaning as the quantifier of the maximum advantage in binary channel discrimination tasks. Finally, we show that several classes of channel and state discrimination tasks can form complete families of monotones fully characterizing the transformations of states and measurements under any chosen class of free operations. Our results establish a fundamental connection between operational tasks of discrimination and core concepts of resource theories, valid for all physical theories with no additional assumptions about the structure of the GPT required.

26 + 3 pages, 1 figure, published version

References in corpus (114)

• Quantum entanglement
• Quantifying Coherence
• Quantum Coherence as a Resource
• The classical-quantum boundary for correlations: discord and related measures
• Fundamental Limits of Repeaterless Quantum Communications
• General Benchmarks for Quantum Repeaters
• Quantum Resource Theories
• Conditions for a class of entanglement transformations
• Entanglement and non-Markovianity of quantum evolutions
• Fundamental limitations for quantum and nano thermodynamics
• Entanglement monotones
• The second laws of quantum thermodynamics
• The European Quantum Technologies Roadmap
• The operational meaning of min- and max-entropy
• The Resource Theory of Quantum States Out of Thermal Equilibrium
• Informational derivation of Quantum Theory
• Robustness of entanglement
• Robustness of coherence: An operational and observable measure of quantum coherence
• The Resource Theory of Stabilizer Computation
• Min- and Max- Relative Entropies and a New Entanglement Monotone
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• Probabilistic theories with purification
• The resource theory of quantum reference frames: manipulations and monotones
• On the Entangling Power of Quantum Evolutions
• Quantum State Discrimination
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Quantum Circuits Architecture
• Quantum Data Hiding
• The general structure of quantum resource theories
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Transforming quantum operations: quantum supermaps
• Quantum state discrimination and its applications
• A derivation of quantum theory from physical requirements
• A mathematical theory of resources
• Statistical distinguishability between unitary operations
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Robustness of asymmetry and coherence of quantum states
• (Quantumness in the context of) Resource Theories
• Hiding bits in Bell states
• Resource theory of quantum non-Gaussianity and Wigner negativity
• All Entangled Quantum States Are Nonlocal
• Quantifying Entanglement with Witness Operators
• Max- relative entropy of coherence: an operational coherence measure
• Quantitative entanglement witnesses
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• Convex resource theory of non-Gaussianity
• Simulating positive-operator-valued measures with projective measurements
• Quantum information and precision measurement
• Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
• How robust is a quantum gate in the presence of noise?
• Genralized Robustness of Entanglement
• Quantifying Superposition
• The resource theory of steering
• All entangled states are useful for channel discrimination
• Resource Destroying Maps
• Quantifying quantum resources with conic programming
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Comparison of Quantum Channels by Superchannels
• One-shot coherence distillation
• Quantifying Operations with an Application to Coherence
• Quantifying magic for multi-qubit operations
• Higher-order interference and single-system postulates characterizing quantum theory
• Gaussian quantum resource theories
• Convex geometry of quantum resource quantification
• A resource theory of quantum memories and their faithful verification with minimal assumptions
• Clean Positive Operator Valued Measures
• Resource Theory of Coherence - Beyond States
• A reversible theory of entanglement and its relation to the second law
• Using and reusing coherence to realize quantum processes
• Robustness of Measurement, discrimination games and accessible information
• Noise Robustness of the Incompatibility of Quantum Measurements
• Resource theory of non-Gaussian operations
• 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
• On the existence of physical transformations between sets of quantum states
• Quantifying resource in catalytic resource theory
• Robustness of incompatibility for quantum devices
• Operational framework for quantum measurement simulability
• Comparison of quantum statistical models: equivalent conditions for sufficiency
• Distinguishability Measures and Entropies for General Probabilistic Theories
• Hilbert's projective metric in quantum information theory
• Quartic quantum theory: an extension of the standard quantum mechanics
• Quantum Relative Lorenz Curves
• Entanglement of a bipartite channel
• Smooth Max-Information as One-Shot Generalization for Mutual Information
• Ultimate data hiding in quantum mechanics and beyond
• Quantifying the resource content of quantum channels: An operational approach
• Entanglement cost and quantum channel simulation
• Entanglement and thermodynamics in general probabilistic theories
• More entanglement implies higher performance in tailored channel discrimination tasks
• State discrimination with post-measurement information and incompatibility of quantum measurements
• Simulating all quantum measurements using only projective measurements and postselection
• Degradable channels, less noisy channels, and quantum statistical morphisms: an equivalence relation
• Computation in generalised probabilistic theories
• Simulability of observables in general probabilistic theories
• Microcanonical thermodynamics in general physical theories
• Operational axioms for diagonalizing states
• Resource theories of knowledge
• Disentanglement Cost of Quantum States
• Base norms and discrimination of generalized quantum channels
• Structure of Optimal State Discrimination in Generalized Probabilistic Theories
• Entanglement activation and the robustness of quantum correlations
• Universal gaps for XOR games from estimates on tensor norm ratios
• Non-classical correlations in quantum mechanics and beyond
• Some notes on the robustness of k-coherence and k-entanglement
• Entanglement as an axiomatic foundation for statistical mechanics
• A quantum version of randomization criterion
• Diagonal quantum discord
• Information-theoretic foundations of thermodynamics in general probabilistic theories
• Operational Resource Theory of Non-Markovianity

Cited by in corpus (143)

• Operational Resource Theory of Imaginarity
• Operational Resource Theory of Quantum Channels
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Resource theory of imaginarity: Quantification and state conversion
• One-Shot Operational Quantum Resource Theory
• No-Go Theorems for Quantum Resource Purification
• General probabilistic theories: An introduction
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Benchmarking one-shot distillation in general quantum resource theories
• Application of the Resource Theory of Channels to Communication Scenarios
• Resource theory of asymmetric distinguishability for quantum channels
• Catalytic quantum teleportation and beyond
• On the Role of Coherence in Shor's Algorithm
• All quantum resources provide an advantage in exclusion tasks
• A chain rule for the quantum relative entropy
• Optimal resource cost for error mitigation
• The type-independent resource theory of local operations and shared randomness
• Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
• Skew informations from an operational view via resource theory of asymmetry
• Catalysis of entanglement and other quantum resources
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Resource speed limits: Maximal rate of resource variation
• Probabilistic transformations of quantum resources
• Quantifying Quantumness of Channels Without Entanglement
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Universal and Operational Benchmarking of Quantum Memories
• Operational quantification of continuous-variable quantum resources
• Type-independent Characterization of Spacelike Separated Resources
• Entanglement and coherence in Bernstein-Vazirani algorithm
• Framework for resource quantification in infinite-dimensional general probabilistic theories
• Fisher information universally identifies quantum resources
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• One-Shot Manipulation of Dynamical Quantum Resources
• Tight constraints on probabilistic convertibility of quantum states
• Operational characterization of incompatibility of quantum channels with quantum state discrimination
• Resource Preservability
• Quantification of quantum dynamics with input-output games
• Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming
• Quantum Channel Marginal Problem
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Quantum marginal problem and incompatibility
• Resource theory of quantum uncomplexity
• Is there a finite complete set of monotones in any quantum resource theory?
• Quantifying dynamical coherence with dynamical entanglement
• $\alpha$-Logarithmic negativity
• A universal scheme for robust self-testing in the prepare-and-measure scenario
• Universal limitations on implementing resourceful unitary evolutions
• Postquantum common-cause channels: the resource theory of local operations and shared entanglement
• Communication, Dynamical Resource Theory, and Thermodynamics
• Coherence of operations and interferometry
• Witnessing non-objectivity in the framework of strong quantum Darwinism
• Inequalities witnessing coherence, nonlocality, and contextuality
• Resource theory of superposition: State transformations
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Multi-object operational tasks for convex quantum resource theories
• Monotones in General Resource Theories
• Coherence manipulation with dephasing-covariant operations
• Device-independent quantification of measurement incompatibility
• 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
• Virtual quantum resource distillation: General framework and applications
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Quantifying imaginarity in terms of pure-state imaginarity
• Incompatibility as a resource for programmable quantum instruments
• Characterizing symmetry-protected thermal equilibrium by work extraction
• A complete and operational resource theory of measurement sharpness
• The operational significance of the quantum resource theory of Buscemi nonlocality
• Quantum advantage for noisy channel discrimination
• Testing quantum theory by generalizing noncontextuality
• Classification and reconstruction of optical quantum states with deep neural networks
• One-shot manipulation of entanglement for quantum channels
• A general theory of comparison of quantum channels (and beyond)
• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• 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
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Local Quantum State Marking
• Information and disturbance in operational probabilistic theories
• Universal structure of objective states in all fundamental causal theories
• Resource Marginal Problems
• Quantum Telescopy Clock Games
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Distance-based resource quantification for sets of quantum measurements
• Perfect discrimination of quantum measurements using entangled systems
• Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure
• Quantum Hypothesis Testing with Group Structure
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• Compositional resource theories of coherence
• Building Multiple Access Channels with a Single Particle
• Resource engines
• Weight of informativeness, state exclusion games and excludible information
• Black Box Work Extraction and Composite Hypothesis Testing
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Classically Replaceable Operations
• Quantifying entanglement preservability of experimental processes
• Quantum information theoretic approach to the hard problem of consciousness
• An operational definition of quantum information scrambling
• Covariant influences for finite discrete dynamical systems
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Quantum process discrimination with restricted strategies
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Projective robustness for quantum channels and measurements and their operational significance
• Optimal allocation of quantum resources
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Informational non-equilibrium concentration
• Completeness Stability of Quantum Measurements
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Single-shot entanglement manipulation of states and channels revisited
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Process tensor distinguishability measures
• Multi-object operational tasks for measurement incompatibility
• Improving quantum channel discrimination with resourceful states
• Coherence as a resource for phase estimation
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• Number of quantum measurement outcomes as a resource
• Weight-based measure of quantum memory as a universal and operational benchmark
• Categories of Brègman operations and epistemic (co)monads
• Complete characterisation of state conversions by work extraction
• Programming of channels in generalized probabilistic theories
• Squashed quantum non-Markovianity: a measure of genuine quantum non-Markovianity in states
• Entropic and operational characterizations of dynamic quantum resources
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Resource theory of interactive quantum instruments
• Golden states in resource theory of superposition
• Detecting quantum resources in a semi-device independent framework
• State convertibility under genuinely incoherent operations
• All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
• An operational characterization of infinite-dimensional quantum resources
• Symmetric channel verification for purifying noisy quantum channels
• Detector entanglement: Quasidistributions for Bell-state measurements
• Thermodynamic criteria for signaling in quantum channels
• Online identification of symmetric pure states
• General quantum resources providing advantages in work-extraction tasks
• The entropy of quantum causal networks
• Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states
• Sharing quantum indistinguishability with multiple parties
• Dephasing superchannels
• Convexity of noncontextual wirings and how they order the set of correlations
• Quantifying coherence of quantum measurements