Framework for resource quantification in infinite-dimensional general probabilistic theories
arXiv:2009.11313 · doi:10.1103/PhysRevA.103.032424
Abstract
Resource theories provide a general framework for the characterization of properties of physical systems in quantum mechanics and beyond. Here, we introduce methods for the quantification of resources in general probabilistic theories (GPTs), focusing in particular on the technical issues associated with infinite-dimensional state spaces. We define a universal resource quantifier based on the robustness measure, and show it to admit a direct operational meaning: in any GPT, it quantifies the advantage that a given resource state enables in channel discrimination tasks over all resourceless states. We show that the robustness acts as a faithful and strongly monotonic measure in any resource theory described by a convex and closed set of free states, and can be computed through a convex conic optimization problem. Specializing to continuous-variable quantum mechanics, we obtain additional bounds and relations, allowing an efficient computation of the measure and comparison with other monotones. We demonstrate applications of the robustness to several resources of physical relevance: optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence. In particular, we establish exact expressions for various classes of states, including Fock states and squeezed states in the resource theory of nonclassicality and general pure states in the resource theory of entanglement, as well as tight bounds applicable in general cases.
arXiv comment32 pages. Companion paper to "Operational quantification of continuous-variable quantum resources" arXiv:2009.11302. v3: accepted version; title shortened
References in corpus (97)
- Quantum entanglement
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Concentrating Partial Entanglement by Local Operations
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Quantifying Coherence
- Quantum Coherence as a Resource
- Quantum Resource Theories
- Quantum computation over continuous variables
- Advances in Photonic Quantum Sensing
- Entanglement monotones
- Quantum Illumination with Gaussian States
- On the impossibility of distilling Gaussian states with Gaussian operations
- Robustness of entanglement
- Robustness of coherence: An operational and observable measure of quantum coherence
- The characterization of Gaussian operations and Distillation of Gaussian States
- Entanglement by a beam splitter: nonclassicality as a prerequisite for entanglement
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- Coding Theorem and Strong Converse for Quantum Channels
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Positive Wigner functions render classical simulation of quantum computation efficient
- Probabilistic theories with purification
- Quantum State Discrimination
- Application of a resource theory for magic states to fault-tolerant quantum computing
- The general structure of quantum resource theories
- Quantum state discrimination and its applications
- A No-Go Theorem for Gaussian Quantum Error Correction
- A computable measure of nonclassicality for light
- 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
- Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
- (Quantumness in the context of) Resource Theories
- Resource theory of quantum non-Gaussianity and Wigner negativity
- Quantifying Entanglement with Witness Operators
- Estimating outcome probabilities of quantum circuits using quasiprobabilities
- Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
- Quantifying non-Gaussianity for quantum information
- Entanglement Theory and the Second Law of Thermodynamics
- General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
- Convex resource theory of non-Gaussianity
- A theorem for the beam splitter entangler
- Quantum information and precision measurement
- Nonclassicality as a Quantifiable Resource for Quantum Metrology
- How robust is a quantum gate in the presence of noise?
- Genralized Robustness of Entanglement
- Quantifying quantum resources with conic programming
- Operational Advantage of Quantum Resources in Subchannel Discrimination
- On the quantification of entanglement in infinite-dimensional quantum systems
- Quantifying Coherence in Infinite Dimensional Systems
- Higher-order interference and single-system postulates characterizing quantum theory
- A Generalization of Quantum Stein's Lemma
- Stellar representation of non-Gaussian quantum states
- Gaussian quantum resource theories
- One-Shot Operational Quantum Resource Theory
- Convex geometry of quantum resource quantification
- A reversible theory of entanglement and its relation to the second law
- Operational resource theory of continuous-variable nonclassicality
- Robustness of Measurement, discrimination games and accessible information
- Operational relevance of resource theories of quantum measurements
- Benchmarking one-shot distillation in general quantum resource theories
- Relative entropy is an exact measure of non-Gaussianity
- Quantifying resource in catalytic resource theory
- All quantum resources provide an advantage in exclusion tasks
- Distinguishability Measures and Entropies for General Probabilistic Theories
- A no-go theorem on the nature of the gravitational field beyond quantum theory
- Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
- Ultimate data hiding in quantum mechanics and beyond
- Entanglement and thermodynamics in general probabilistic theories
- Negativity of quasiprobability distributions as a measure of nonclassicality
- Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis
- Universal and Operational Benchmarking of Quantum Memories
- More entanglement implies higher performance in tailored channel discrimination tasks
- On the measure of nonclassicality of field states
- Coherence and entanglement measures based on Rényi relative entropies
- The Smooth Entropy Formalism for von Neumann Algebras
- Phase-space inequalities beyond negativities
- Operational quantification of continuous-variable quantum resources
- Nonclassical distance in multimode bosonic systems
- The first law of general quantum resource theories
- Quantum non-Gaussianity and secure quantum communication
- Microcanonical thermodynamics in general physical theories
- Quantification of quantum dynamics with input-output games
- Separability and Entanglement-Breaking in Infinite Dimensions
- General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
- Resource theories of knowledge
- A new class of entanglement measures
- Base norms and discrimination of generalized quantum channels
- Asymptotic state transformations of continuous variable resources
- Structure of Optimal State Discrimination in Generalized Probabilistic Theories
- Adaptation of the Alicki-Fannes-Winter method for the set of states with bounded energy and its use
- Non-classical correlations in quantum mechanics and beyond
- On properties of the space of quantum states and their application to construction of entanglement monotones
- Assisted concentration of Gaussian resources
- Entanglement-assisted capacity of constrained quantum channel
- A geometric measure of non-classicality
Cited by in corpus (24)
- General probabilistic theories: An introduction
- Operational quantification of continuous-variable quantum resources
- Tight constraints on probabilistic convertibility of quantum states
- Asymptotic state transformations of continuous variable resources
- Quantum data hiding with continuous variable systems
- Quantifying non-Gaussianity of a quantum state by the negative entropy of quadrature distributions
- Every quantum helps: Operational advantage of quantum resources beyond convexity
- Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
- General Probabilistic Theories with a Gleason-type Theorem
- Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
- Continuity of characteristics of composite quantum systems
- Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
- One-shot manipulation of entanglement for quantum channels
- Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
- Classical simulation and quantum resource theory of non-Gaussian optics
- Continuity of robustness measures in quantum resource theories
- Entanglement cost for infinite-dimensional physical systems
- Computable lower bounds on the entanglement cost of quantum channels
- Projective robustness for quantum channels and measurements and their operational significance
- Improving quantum channel discrimination with resourceful states
- An operational characterization of infinite-dimensional quantum resources
- All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
- Entropic and operational characterizations of dynamic quantum resources
- Impact of quadrature measurement on quantum coherence