Quantum resource theories in the single-shot regime

Abstract

One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions (NSC) that determine whether one resource can be converted to another by the set of free operations. Here we find such NSC for a large class of quantum resource theories which we call affine resource theories (ART). ARTs include the resource theories of athermality, asymmetry, and coherence, but not entanglement. Remarkably, the NSC can be expressed as a family of inequalities between resource monotones (quantifiers) that are given in terms of the conditional min entropy. The set of free operations is taken to be (1) the maximal set (i.e. consists of all resource non-generating (RNG) quantum channels) or (2) the self-dual set of free operations (i.e. consists of all RNG maps for which the dual map is also RNG). As an example, we apply our results to quantum thermodynamics with Gibbs preserving operations, and several other ARTs. Finally, we discuss the applications of these results to resource theories that are not affine, and along the way, provide the NSC that a quantum resource theory consists of a resource destroying map.

5 pages (main text)+11 pages (appendix), 1 figure, completely restructured with simple applications presented first, notations simplified, new references added

References in corpus (12)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• The resource theory of quantum reference frames: manipulations and monotones
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Entanglement Theory and the Second Law of Thermodynamics
• Resource Destroying Maps
• Quantum Relative Lorenz Curves
• Multi-particle entanglement manipulation under positive partial transpose preserving operations
• Simulating Symmetric Time Evolution With Local Operations
• Entanglement monotones and transformations of symmetric bipartite states

Cited by in corpus (61)

• Quantum Resource Theories
• Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
• Resource theory of quantum non-Gaussianity and Wigner negativity
• An introductory review of the resource theory approach to thermodynamics
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Quantifying quantum resources with conic programming
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Quantifying the Imaginarity of Quantum Mechanics
• One-shot coherence distillation
• Gaussian quantum resource theories
• One-Shot Operational Quantum Resource Theory
• Convex geometry of quantum resource quantification
• MBL-mobile: Quantum engine based on many-body localization
• One-Shot Coherence Dilution
• Application of the Resource Theory of Channels to Communication Scenarios
• Benchmarking one-shot distillation in general quantum resource theories
• Quantifying resource in catalytic resource theory
• Dynamical Entanglement
• Entanglement of a bipartite channel
• Third Law of Thermodynamics as a Single Inequality
• Skew informations from an operational view via resource theory of asymmetry
• Probabilistic transformations of quantum resources
• Quantification and manipulation of magic states
• Quantum coherence and state conversion: theory and experiment
• Non-asymptotic assisted distillation of quantum coherence
• Operational quantification of continuous-variable quantum resources
• Quantum advantage in simulating stochastic processes
• Fisher information universally identifies quantum resources
• One-Shot Manipulation of Dynamical Quantum Resources
• Resource Preservability
• Tight constraints on probabilistic convertibility of quantum states
• Encoding classical information into quantum resources
• Is there a finite complete set of monotones in any quantum resource theory?
• Flag Additivity in Quantum Resource Theories
• Universal limitations on implementing resourceful unitary evolutions
• Approximate reversal of quantum Gaussian dynamics
• Communication, Dynamical Resource Theory, and Thermodynamics
• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• Nonlocal Advantages of Quantum Imaginarity
• Resource theory of superposition: State transformations
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• The variance of relative surprisal as single-shot quantifier
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Moderate deviation analysis of majorisation-based resource interconversion
• Overcoming entropic limitations on asymptotic state transformations through probabilistic protocols
• Compositional resource theories of coherence
• Accessible bounds for general quantum resources
• Censorship of Quantum Resources in Quantum Networks
• The resource theory of coherence for quantum channels
• Optimization free measures of quantum resources
• Quantum Causal Structure and Quantum Thermodynamics
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Classically Replaceable Operations
• Unbreakable and breakable quantum censorship
• The Complementary Information Principle of Quantum Mechanics
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Censorship of quantum resources against catalytic account sharing
• Methods of constructing superposition measures
• Entropic and operational characterizations of dynamic quantum resources
• Mathematical methods for resource-based type theories
• Experimental certification of the nonlocal advantages of quantum imaginarity