# 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.

## 132 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…

### Hidden variable model for quantum computation with magic states on 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 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.

### Determinism and Computational Power of Real Measurement-Based Quantum Computation

- Computer ScienceFCT
- 2017

It is proved however that Pauli flow is necessary for determinism in the real MBQC model, an interesting and useful fragment ofMBQC.

### 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 SciencePhysical Review Letters
- 2022

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.

## References

SHOWING 1-10 OF 59 REFERENCES

### A 2 rebit gate universal for quantum computing

- Physics, Computer Science
- 2002

It is shown, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes, which allows us to identify a 2-qubit gate which is universal for quantum computing, although it cannot be used to perform arbitrary unitary transformations.

### A one-way quantum computer.

- Physics, Computer SciencePhysical review letters
- 2001

A scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states, which are thus one-way quantum computers and the measurements form the program.

### Computational power of correlations.

- PhysicsPhysical review letters
- 2009

This work exposes an intriguing relationship between the violation of local realistic models and the computational power of entangled resource states in measurement-based quantum computation.

### Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)

- Physics
- 2005

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.…

### Fault-tolerant quantum computation with high threshold in two dimensions.

- Physics, Computer SciencePhysical review letters
- 2007

We present a scheme of fault-tolerant quantum computation for a local architecture in two spatial dimensions. The error threshold is 0.75% for each source in an error model with preparation, gate,…

### Corrigendum: Negative quasi-probability as a resource for quantum computation

- Physics
- 2012

The full text of this article is available in the PDF provided.

### Efficient classical simulation of continuous variable quantum information processes.

- Physics, MathematicsPhysical review letters
- 2002

It is obtained that any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.

### On the Problem of Hidden Variables in Quantum Mechanics

- Physics
- 1966

The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. It…

### The resource theory of stabilizer quantum computation

- Physics
- 2013

A resource theory, analogous to the theory of entanglement, is developed that is relevant for fault-tolerant stabilizer computation and introduces two quantitative measures for the amount of non-stabilizer resource, including the sum of the negative entries of the discrete Wigner representation of a quantum state.