All quantum resources provide an advantage in exclusion tasks
arXiv:1909.10484 · doi:10.1103/PhysRevLett.125.110402
Abstract
A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterisation of the convex components and corresponding weights of such devices.
arXiv comment8 pages, comments are welcome
References in corpus (23)
- Quantum Resource Theories
- Operational Resource Theory of Coherence
- Robustness of coherence: An operational and observable measure of quantum coherence
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Relating the Resource Theories of Entanglement and Quantum Coherence
- General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
- One-to-one mapping between steering and joint measurability problems
- The resource theory of steering
- 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
- Quantum Incompatibility Witnesses
- Convex geometry of quantum resource quantification
- The WAY theorem and the quantum resource theory of asymmetry
- Demonstration of Einstein-Podolsky-Rosen Steering with Enhanced Subchannel Discrimination
- A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
- Operational relevance of resource theories of quantum measurements
- Incompatibility robustness of quantum measurements: a unified framework
- Verifying the quantumness of a channel with an untrusted device
- Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
- Quantification of quantum dynamics with input-output games
- On coexistence and joint measurability of rank-1 quantum observables
- Weight of informativeness, state exclusion games and excludible information
Cited by in corpus (52)
- Quantum Steering
- Incompatible measurements in quantum information science
- Experimental progress on quantum coherence: detection, quantification, and manipulation
- On the Role of Coherence in Shor's Algorithm
- Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
- Fundamental limitations on distillation of quantum channel resources
- Probabilistic transformations of quantum resources
- No-go theorems for quantum resource purification II: new approach and channel theory
- Operational quantification of continuous-variable quantum resources
- Framework for resource quantification in infinite-dimensional general probabilistic theories
- Fisher information universally identifies quantum resources
- Tight constraints on probabilistic convertibility of quantum states
- Coherence of operations and interferometry
- Simulability of high-dimensional quantum measurements
- One-Shot Yield-Cost Relations in General Quantum Resource Theories
- Every quantum helps: Operational advantage of quantum resources beyond convexity
- Characterisation of quantum betting tasks in terms of Arimoto mutual information
- Incompatibility as a resource for programmable quantum instruments
- The operational significance of the quantum resource theory of Buscemi nonlocality
- Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories
- Quantifying dynamical coherence with coherence measures
- Limitations of Classically-Simulable Measurements for Quantum State Discrimination
- Thermodynamic Approach to Quantifying Incompatible Instruments
- Estimate distillable entanglement and quantum capacity by squeezing useless entanglement
- Distance-based resource quantification for sets of quantum measurements
- Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
- Operational Interpretation of the Choi Rank Through k-State Exclusion
- Distributed quantum incompatibility
- Quantum guessing games with posterior information
- Unified Approach to Witness Nonentanglement-Breaking Quantum Channels
- Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
- Projective robustness for quantum channels and measurements and their operational significance
- Single-shot Distinguishability and Anti-distinguishability of Quantum Measurements
- Coherence as a resource for phase estimation
- Quantifying imaginarity of quantum operations
- The pretty bad measurement
- Multi-object operational tasks for measurement incompatibility
- Complete characterisation of state conversions by work extraction
- How contextuality and antidistinguishability are related
- Weight-based measure of quantum memory as a universal and operational benchmark
- Symmetric channel verification for purifying noisy quantum channels
- Quantum state exclusion for group-generated ensembles of pure states
- An operational characterization of infinite-dimensional quantum resources
- Compressing continuous variable quantum measurements
- Resource theory of interactive quantum instruments
- Semi-device-independent certification of number of measurements
- General quantum resources providing advantages in work-extraction tasks
- On compatibility of binary qubit measurements
- Distance-based measures and Epsilon-measures for measurement-based quantum resources
- Random Exclusion Codes: Quantum Advantages of Single-Shot Communication
- Single-shot antidistinguishability of unitary operations
- Barycentric decomposition for quantum instruments