| Summary: | We study the resources necessary for quantum computation with rebits (qubit states with real amplitudes in the standard basis). We introduce a scheme for universal quantum computation by state injection, and define a Wigner function appropriate for this scheme. We show that the Wigner function obeys a Hudson’s theorem and transforms covariantly under CSS-ness preserving unitary gates; these results allows us to establish that Wigner function negativity is necessary for quantum computation. Furthermore, we establish contextuality as another necessary computational resource. We show that in contrast with the case of qudits [M. Howard et al., Nature 510, 351 (2014)], negativity does not imply contextuality. We discuss state independent contextuality and why it does not arise in our computational scheme. === Science, Faculty of === Physics and Astronomy, Department of === Graduate
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