# Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

@article{Kocia2017DiscreteWF, title={Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states}, author={Lucas Kocia and Peter Love}, journal={Physical Review A}, year={2017}, volume={96}, pages={062134} }

We show that Clifford operations on qubit stabilizer states are non-contextual and can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two---producing an exterior, or Grassmann, algebra---which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 41 REFERENCES

## Multiqubit Clifford groups are unitary 3-designs

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Contextuality Supplies the Magic for Quantum Computation

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Erratum: Non-negative subtheories and quasiprobability representations of qubits [Phys. Rev. A 85 , 062121 (2012)]

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Negativity and contextuality are equivalent notions of nonclassicality.

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Improved Simulation of Stabilizer Circuits

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## The Weyl representation in classical and quantum mechanics

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## A Wigner-function formulation of finite-state quantum mechanics

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Particle spin dynamics as the grassmann variant of classical mechanics

VIEW 14 EXCERPTS

HIGHLY INFLUENTIAL