# Wigner Function Negativity and Contextuality in Quantum Computation on Rebits

@article{Delfosse2014WignerFN, title={Wigner Function Negativity and Contextuality in Quantum Computation on Rebits}, author={Nicolas Delfosse and Philippe Allard Gu{\'e}rin and Jacob Bian and Robert Raussendorf}, journal={Physical Review X}, year={2014}, volume={5}, pages={021003} }

Quantum computation commonly relies on qubits, but rebits---states with real density matrices---can be used as well. Researchers show how the contextuality of two-level states is necessary for quantum computation.

## 129 Citations

### Contextuality and Wigner-function negativity in qubit quantum computation

- Physics
- 2017

We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. These…

### Equivalence between contextuality and negativity of the Wigner function for qudits

- Physics
- 2016

Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality for…

### Contextuality as a resource for qubit quantum computation

- Physics
- 2015

We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a…

### Hidden Variable Model for Quantum Computation with Magic States on Any Number of Qudits of Any Dimension

- Physics
- 2021

It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden…

### Contextuality as a Resource for Models of Quantum Computation with Qubits.

- PhysicsPhysical review letters
- 2017

This work establishes contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits for measurement-based quantum computation.

### Simulation of qubit quantum circuits via Pauli propagation

- Computer Science, PhysicsPhysical Review A
- 2019

Novel algorithms to estimate outcomes for qubit quantum circuits using probability distributions constructed from Bloch vectors are presented, paralleling previously known algorithms that use the discrete Wigner function for qutrits.

### Topological proofs of contextuality in quantum mechanics

- Physics
- 2017

We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies…

### Necessary and Sufficient Condition for Quantum State-Independent Contextuality.

- MathematicsPhysical review letters
- 2015

This work solves the problem of whether a set of quantum tests reveals state-independent contextuality and uses this result to identify the simplest set of the minimal dimension and shows that identifying state- independent contextuality graphs is not sufficient.

### Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements

- Physics, Computer Science
- 2021

This work shows that contextuality and Wigner negativity are in fact equivalent for the standard models of continuous-variable quantum computing, and sheds light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

### Bosonic indistinguishability-dependent contextuality

- PhysicsPhysical Review A
- 2022

We uncover a form of quantum contextuality that connects maximal contextuality to boson indistinguihability in a similar way maximal nonlocality with respect to the Clauser-Horne-Shimony-Holt Bell…

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