On nonlocality as a resource theory and nonlocality measures

Abstract

With the advent of device independent quantum information processing, nonlocality is nowadays regarded as a resource to implement various tasks. On the analogy of entanglement theory we approach nonlocality from this perspective. In order to do so, we analyze in full detail the operations that can be implemented in this scenario and under which nonlocality cannot increase. This provides a theoretical ground to study how to order and quantify nonlocal behaviours. Finally, we review several nonlocality measures and discuss their validity from this point of view.

21 pages. For the special issue "50 years of Bell's theorem"

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Cited by in corpus (74)

• Quantum Resource Theories
• The resource theory of steering
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• Quantifying the Imaginarity of Quantum Mechanics
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• Gaussian quantum resource theories
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Robustness of Measurement, discrimination games and accessible information
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• Operational framework for quantum measurement simulability
• Genuine multipartite nonlocality is intrinsic to quantum networks
• Simple method for experimentally testing any form of quantum contextuality
• 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
• Quantifying Bell non-locality with the trace distance
• There is no anomaly in the nonlocality of two entangled qutrits
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Fundamental limits on key rates in device-independent quantum key distribution
• Steering maps and their application to dimension-bounded steering
• Noncontextual wirings
• Resource theory of contextuality for arbitrary prepare-and-measure experiments
• Measures of imaginarity and quantum state order
• Type-independent Characterization of Spacelike Separated Resources
• Axiomatic approach to contextuality and nonlocality
• Nonlocality free wirings and the distinguishability between Bell boxes
• One-Shot Manipulation of Dynamical Quantum Resources
• Imaginarity of Gaussian states
• Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
• Optimal Extensions of Resource Measures and their Applications
• Resilience of realism-based nonlocality to local disturbance
• Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages
• Memory cost for simulating all quantum correlations of the Peres-Mermin scenario
• Multi-object operational tasks for convex quantum resource theories
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
• Neither Contextuality nor Nonlocality Admits Catalysts
• Experimental quantification of spatial correlations in quantum dynamics
• Quantifying Spatial Correlations of General Quantum Dynamics
• The operational advantages provided by non-classical teleportation
• Distilling Nonlocality in Quantum Correlations
• Maximal Violation of a Broad Class of Bell Inequalities and Its Implications on Self-Testing
• Quantum nonlocality in extended theories of gravity
• Nonlocality Distillation and Quantum Voids
• Quantum Bell Nonlocality is Entanglement
• Resource theory of heat and work with non-commuting charges
• Resource Marginal Problems
• Quantifying necessary quantum resources for nonlocality
• Geometric-Like imaginarity: quantification and state conversion
• Realism-based nonlocality: Invariance under local unitary operations and asymptotic decay for thermal correlated states
• Quantum Nonlocality: Multi-copy Resource Inter-convertibility & Their Asymptotic Inequivalence
• Distance-based resource quantification for sets of quantum measurements
• Accessible bounds for general quantum resources
• Quantifying Bell nonlocality of a pure two-qudit state via its entanglement
• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• Quantifying nonlocality as a resource for device-independent quantum key distribution
• Bell non-locality using tensor networks and sparse recovery
• Multipartite Nonlocality in Clifford Networks
• Every non-signalling channel is common-cause realizable
• Quantifying the imaginarity via different distance measures
• Operational approach to the topological structure of the physical space
• Optimal allocation of quantum resources
• Exposure of subtle multipartite quantum nonlocality
• Error-free interconversion of nonlocal boxes
• Strength of the nonlocality of two-qubit entangled state and its applications
• Certifying nonlocal properties of noisy quantum operations
• Multi-object operational tasks for measurement incompatibility
• Quantum correlation generation capability of experimental processes
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• The genuinely multipartite nonlocality of graph states is model-dependent
• Events in quantum mechanics are maximally non-absolute
• Inter-qubit correlation dynamics driven by mutual interactions
• Convexity of noncontextual wirings and how they order the set of correlations
• Distance-based measures and Epsilon-measures for measurement-based quantum resources