Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios

Abstract

We employ the resource theory of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework simplifies proofs of quantum contextuality in complex scenarios and strengthens existing arguments regarding robustness of experimental implementations. As a case study, we demonstrate quantum contextuality associated with any nontrivial noncontextuality inequality for a class of useful scenarios by noticing a connection between the resource theory and measurement simulability. Additionally, we expose a formal composition rule that allows engineering complex scenarios from simpler ones. This approach provides insights into the noncontextual polytope structure for complex scenarios and facilitates the identification of possible quantum violations of noncontextuality inequalities.

arXiv comment11 pages (+9 page Appendix), 2 figures (+1 figure and 3 tables in appendix)

References in corpus (53)

• Quantifying Coherence
• Bell nonlocality
• Quantum Coherence as a Resource
• Quantum Resource Theories
• Contextuality for preparations, transformations, and unsharp measurements
• Quantum Darwinism
• Einstein, incompleteness, and the epistemic view of quantum states
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• A mathematical theory of resources
• Trading classical and quantum computational resources
• An experimental test of noncontextuality without unwarranted idealizations
• Preparation contextuality powers parity-oblivious multiplexing
• Classical randomness in quantum measurements
• Simulating positive-operator-valued measures with projective measurements
• Quantifying Superposition
• The contextual fraction as a measure of contextuality
• Generic emergence of classical features in quantum Darwinism
• Lifting Bell inequalities
• Contextual advantage for state discrimination
• Quantifying Contextuality
• Maximally epistemic interpretations of the quantum state and contextuality
• Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response
• From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism
• Optimal bounds for parity-oblivious random access codes
• Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
• On the Role of Coherence in Shor's Algorithm
• Operational framework for quantum measurement simulability
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
• Contextual advantage for state-dependent cloning
• A hidden variable model for universal quantum computation with magic states on qubits
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Robust preparation noncontextuality inequalities in the simplest scenario
• Resource theory of contextuality for arbitrary prepare-and-measure experiments
• Noncontextual wirings
• Axiomatic approach to contextuality and nonlocality
• Entanglement and coherence in Bernstein-Vazirani algorithm
• From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities
• Simulability of observables in general probabilistic theories
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Distributed sampling, quantum communication witnesses, and measurement incompatibility
• Foundations of quantum theory and quantum information applications
• An invertible map between Bell non-local and contextuality scenarios
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Inequalities witnessing coherence, nonlocality, and contextuality
• Contextuality bounds the efficiency of classical simulation of quantum processes
• Bounding and simulating contextual correlations in quantum theory
• Neither Contextuality nor Nonlocality Admits Catalysts
• Ontological models, preparation contextuality and nonlocality
• Contextuality with vanishing coherence and maximal robustness to dephasing
• Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem
• Contextuality beyond the Kochen-Specker theorem
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• The rank of contextuality

Cited by in corpus (6)

• Coherence and contextuality in a Mach-Zehnder interferometer
• Inequalities witnessing coherence, nonlocality, and contextuality
• Contextuality in anomalous heat flow
• Sufficiency of the counterfactual account of Lüders' rule to rule out ontological models of quantum mechanics
• Contextual advantages across two-state discrimination strategies
• Convexity of noncontextual wirings and how they order the set of correlations