Resource Destroying Maps

Abstract

Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this paper, we propose a general scheme for analyzing resource theories based on resource destroying maps, which leave resource-free states unchanged but erase the resource stored in all other states. We introduce a group of general conditions that determine whether a quantum operation exhibits typical resource-free properties in relation to a given resource destroying map. Our theory reveals fundamental connections among basic elements of resource theories, in particular, free states, free operations, and resource measures. In particular, we define a class of simple resource measures that can be calculated without optimization, and that are monotone nonincreasing under operations that commute with the resource destroying map. We apply our theory to the resources of coherence and quantum correlations (e.g., discord), two prominent features of nonclassicality.

12 pages including Supplemental Material, published version

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Cited by in corpus (104)

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• Operational Resource Theory of Quantum Channels
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• One-Shot Operational Quantum Resource Theory
• No-Go Theorems for Quantum Resource Purification
• Convex geometry of quantum resource quantification
• Resource theory of coherence based on positive-operator-valued measures
• Resource theory of non-Gaussian operations
• Certification and Quantification of Multilevel Quantum Coherence
• Quantum resource theories in the single-shot regime
• Application of the Resource Theory of Channels to Communication Scenarios
• Benchmarking one-shot distillation in general quantum resource theories
• On the Role of Coherence in Shor's Algorithm
• Superconducting-like heat current: Effective cancellation of current-dissipation trade off by quantum coherence
• Coherence and non-classicality of quantum Markov processes
• Dynamical Resource Theory of Quantum Coherence
• Skew informations from an operational view via resource theory of asymmetry
• Quantifying the resource content of quantum channels: An operational approach
• Generic bound coherence under strictly incoherent operations
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Quantifying coherence with respect to general quantum measurements
• No-go theorems for quantum resource purification II: new approach and channel theory
• Measurement-dependent corrections to work distributions arising from quantum coherences
• Operational quantification of continuous-variable quantum resources
• Quantum Entropy and Central Limit Theorem
• Coherence of quantum channels
• Discordlike correlation of bipartite coherence
• Experimental quantification of coherence of a tunable quantum detector
• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• Encoding classical information into quantum resources
• Quantum coherence in a compass chain under an alternating magnetic field
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• The role of coherence during classical and quantum decoherence
• Quantifying dynamical coherence with dynamical entanglement
• Universal limitations on implementing resourceful unitary evolutions
• Quantitative Coherence Witness for Finite Dimensional States
• Quantifying coherence in terms of the pure-state coherence
• Communication, Dynamical Resource Theory, and Thermodynamics
• Of Local Operations and Physical Wires
• Maximum Relative Entropy of Coherence for Quantum Channels
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Coherence of operations and interferometry
• Information-based approach towards a unified resource theory
• Resource theory of superposition: State transformations
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Subtleties of witnessing quantum coherence in non-isolated systems
• Coherence manipulation with dephasing-covariant operations
• Coherence transformations in single qubit systems
• Every quantum helps: Operational advantage of quantum resources beyond convexity
• Universal Method to Estimate Quantum Coherence
• Accessible coherence in open quantum system dynamics
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders
• Experimental Control of the Degree of Non-Classicality via Quantum Coherence
• Preparing tunable Bell-diagonal states on a quantum computer
• Examining the validity of Schatten-$p$-norm-based functionals as coherence measures
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• Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Optimal approximations of available states and a triple uncertainty relation
• Coherence measures based on sandwiched Rényi relative entropy
• Diagonal quantum discord
• Resource Marginal Problems
• Universal structure of objective states in all fundamental causal theories
• Why should we care about quantum discord?
• Accessible bounds for general quantum resources
• The resource theory of coherence for quantum channels
• Censorship of Quantum Resources in Quantum Networks
• Quantifying quantum coherence based on the Tsallis relative operator entropy
• Compositional resource theories of coherence
• Multi-linear Monogamy Relations for Three Qubit States
• Optimization free measures of quantum resources
• Distinguishing classically indistinguishable states and channels
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Predictability as a quantum resource
• Classically Replaceable Operations
• Cone-Restricted Information Theory
• Multipartite Nonlocality in Clifford Networks
• An alternative framework for quantifying coherence of quantum channels
• The role of coherence theory in attractor quantum neural networks
• Role of quantum state texture in probing resource theories and quantum phase transition
• One-shot manipulation of coherence in dynamic quantum resource theory
• Unbreakable and breakable quantum censorship
• Environmental effects on nonlocal correlations
• On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Coherence as a resource for phase estimation
• Methods of constructing superposition measures
• The quantum uncertainty relations of quantum channels
• Work, entropy production, and thermodynamics of information under protocol constraints
• Censorship of quantum resources against catalytic account sharing
• Entropic and operational characterizations of dynamic quantum resources
• What are temporal correlations
• Coherence measures in the strictly incoherent operation framework and its application in the multi-path interferometer
• A resource theory of Maxwell's demons
• The entangling power of non-entangling channels
• Macroscopicity and observational deficit in states, operations, and correlations
• Functoriality of Quantum Resource Theory and Variable-Domain Modal Logic