Wigner function negativity and contextuality in quantum computation on rebits

Understand

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.