Wigner function negativity and contextuality in quantum computation on rebits

Abstract

We describe a universal scheme of quantum computation by state injection on rebits (states with real density matrices). For this scheme, we establish contextuality and Wigner function negativity as computational resources, extending results of [M. Howard et al., Nature 510, 351--355 (2014)] to two-level systems. For this purpose, we define a Wigner function suited to systems of $n$ rebits, and prove a corresponding discrete Hudson's theorem. We introduce contextuality witnesses for rebit states, and discuss the compatibility of our result with state-independent contextuality.

18 + 4 pages

References in corpus (21)

• Fault-tolerant quantum computation by anyons
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Hidden Variables and the Two Theorems of John Bell
• Fault-tolerant quantum computation with high threshold in two dimensions
• Quantum Error Correction and Orthogonal Geometry
• Contextuality supplies the magic for quantum computation
• The Resource Theory of Stabilizer Computation
• Positive Wigner functions render classical simulation of quantum computation efficient
• The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
• Discrete phase space based on finite fields
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Negative Quasi-Probability as a Resource for Quantum Computation
• Graph-Theoretic Approach to Quantum Correlations
• Negativity and contextuality are equivalent notions of nonclassicality
• Contextuality in Measurement-based Quantum Computation
• Computational power of correlations
• Classicality in discrete Wigner functions
• Discrete Wigner functions and quantum computational speedup
• Nonnegative subtheories and quasiprobability representations of qubits
• Quantum Contextuality with Stabilizer States
• Stronger Quantum Correlations with Loophole-free Post-selection

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• Locality-Preserving Logical Operators in Topological Stabiliser Codes
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• Leggett-Garg macrorealism and the quantum nondisturbance conditions
• Significant-loophole-free test of Kochen-Specker contextuality using two species of atomic-ions
• Necessary and sufficient condition for contextuality from incompatibility
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• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Discrete Wigner Formalism for Qubits and Non-Contextuality of Clifford Gates on Qubit Stabilizer States
• Contextuality in phase space
• Quantum correlations from simple assumptions
• Experimental test of contextuality in quantum and classical systems
• Probability representation of quantum dynamics using pseudostochastic maps
• Memory cost of temporal correlations
• Quantum theory allows for absolute maximal contextuality
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Quantum Advantage in Information Retrieval
• Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements
• Contextuality in spin-orbit laser modes
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
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• Contextuality and The Single-Qubit Stabilizer Formalism
• Single-photon quantum contextuality on a chip
• Graph-theoretic strengths of contextuality
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
• State-injection schemes of quantum computation in Spekkens' toy theory
• The role of cohomology in quantum computation with magic states
• Fluctuating work in coherent quantum systems: proposals and limitations
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• Experimental entanglement characterization of two-rebit states
• Necessary Conditions for Extended Noncontextuality in General Sets of Random Variables
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
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• A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
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• Sharp complexity phase transitions generated by entanglement
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• Hierarchies of resources for measurement-based quantum computation
• Experimental demonstration of the connection between quantum contextuality and graph theory
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• Semiclassical Formulation of Gottesman-Knill and Universal Quantum Computation
• On Possibilistic Conditions to Contextuality and Nonlocality
• Experimental test of high-dimensional quantum contextuality based on contextuality concentration
• Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits
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• Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus
• Discrete phase-space mappings, tomographic condition and permutation invariance
• Qubit from the classical collision entropy
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Irreducible magic sets for $n$-qubit systems
• Connecting XOR and XOR* games
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Spread and asymmetry of typical quantum coherence and their inhibition in response to glassy disorder
• Bosonic Indistinguishability-Dependent Contextuality
• A quantum prediction as a collection of epistemically restricted classical predictions
• Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
• Simulating quantum computation: how many "bits" for "it"?
• Strong analog classical simulation of coherent quantum dynamics
• A 3D lattice defect and efficient computations in topological MBQC
• Quantum-to-Classical Transition via Single-Shot Generalized Measurements
• Simulation of quantum computation with magic states via Jordan-Wigner transformations
• Experimental Approach to Demonstrating Contextuality for Qudits
• Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
• Characterization of non-adaptive Clifford channels
• Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes
• General entropic constraints on CSS codes within magic distillation protocols
• The Interplay between Quantum Contextuality and Wigner Negativity
• Certifying Macroscopic Quantum Mechanics via Hypothesis Testing with Finite Data
• Duality theory for Clifford tensor powers
• Noncontextual Pauli Hamiltonians
• All fundamental non-contextuality inequalities are unique