Resource theory of contextuality for arbitrary prepare-and-measure experiments

Abstract

Contextuality has been identified as a potential resource responsible for the quantum advantage in several tasks. It is then necessary to develop a resource-theoretic framework for contextuality, both in its standard and generalized forms. Here we provide a formal resource-theoretic approach for generalized contextuality based on a physically motivated set of free operations with an explicit parametrisation. Then, using an efficient linear programming characterization for the contextual set of prepared-and-measured statistics, we adapt known resource quantifiers for contextuality and nonlocality to obtain natural monotones for generalized contextuality in arbitrary prepare-and-measure experiments.

11 pages, 4 figures. Comments are welcome!

References in corpus (9)

• Almost quantum correlations
• The contextual fraction as a measure of contextuality
• Wigner function negativity and contextuality in quantum computation on rebits
• (Non-)Contextuality of Physical Theories as an Axiom
• All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
• Quantifying Bell non-locality with the trace distance
• Nonlocality free wirings and the distinguishability between Bell boxes
• Contextuality bounds the efficiency of classical simulation of quantum processes
• Contextuality and The Single-Qubit Stabilizer Formalism

Cited by in corpus (24)

• Operational interpretation of weight-based resource quantifiers in convex quantum resource theories of states
• Quantum Advantage from Sequential-Transformation Contextuality
• Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
• One-Shot Manipulation of Dynamical Quantum Resources
• Contextual Subspace Variational Quantum Eigensolver
• Coherence and contextuality in a Mach-Zehnder interferometer
• Inequalities witnessing coherence, nonlocality, and contextuality
• Classical Simulation of Noncontextual Pauli Hamiltonians
• Bounding and simulating contextual correlations in quantum theory
• Noncontextuality Inequalities from Antidistinguishability
• Communication tasks in operational theories
• Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios
• Resource theory of heat and work with non-commuting charges
• Categories of Empirical Models
• Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits
• Contextuality in anomalous heat flow
• Continuous-variable nonlocality and contextuality
• From Quantum Source Compression to Quantum Thermodynamics
• Complementary Resource Relation of Concurrence and Roughness for atwo Qubits State
• Emergence of maximal hidden quantum correlations and its trade-off with the filtering probability in dissipative two-qubit systems
• Robustness of contextuality under different types of noise as quantifiers for parity-oblivious multiplexing tasks
• Operational approach to the topological structure of the physical space
• Emergence of noncontextuality under quantum Darwinism
• Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light