Equivalence between contextuality and negativity of the Wigner function for qudits

Abstract

Contextuality and negativity of the Wigner function are two notions of non-classicality for quantum systems. Howard, Wallman, Veitch and Emerson proved recently that these two notions coincide for qudits in odd prime dimension. This equivalence is particularly important since it promotes contextuality as a ressource that magic states must possess in order to allow for a quantum speed-up. We propose a simple proof of the equivalence between contextuality and negativity of the Wigner function based on character theory. This simplified approach allows us to generalize this equivalence to multiple qudits and to any qudit system of odd local dimension.

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Cited by in corpus (45)

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• Contextuality and Wigner function negativity in qubit quantum computation
• Phase space simulation method for quantum computation with magic states on qubits
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Uniqueness of noncontextual models for stabilizer subtheories
• Quantification and manipulation of magic states
• A hidden variable model for universal quantum computation with magic states on qubits
• Witnessing Wigner Negativity
• Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements
• Qutrit and Ququint Magic States
• Wigner negativity in spin-$j$ systems
• Quantum Advantage in Information Retrieval
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• The role of cohomology in quantum computation with magic states
• A mathematical framework for operational fine tunings
• The axiomatic and the operational approaches to resource theories of magic do not coincide
• Contextual bound states for qudit magic state distillation
• A classical formulation of quantum theory?
• Kenfack Zyczkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit
• Contextuality and the fundamental theorems of quantum mechanics
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Benchmarking of universal qutrit gates
• Quasiprobability distributions with weak measurements
• The Landau Problem and non-Classicality
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• Classifying space for quantum contextuality
• Polytopes of Absolutely Wigner Bounded Spin States
• Signed quantum weight enumerators characterize qubit magic state distillation
• Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
• Wigner's Theorem for stabilizer states and quantum designs
• Harvesting Contextuality from the Vacuum
• Decoherence and Probability
• Exploring the boundary of quantum correlations with a time-domain optical processor
• Symmetries and Wigner representations of operational theories
• Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes
• Spin coherence scale: operator-ordering sensitivity beyond the Heisenberg-Weyl group
• Preparation and Measurement in Quantum Memory Models
• Qudit Clauser-Horne-Shimony-Holt Inequality and Nonlocality from Wigner Negativity
• The Interplay between Quantum Contextuality and Wigner Negativity
• Contextuality from the vacuum