Wigner function negativity and contextuality in quantum computation on rebits

TL;DR

This paper demonstrates that Wigner function negativity and contextuality serve as essential resources for universal quantum computation on rebits, extending prior results to two-level systems and establishing a new framework for their analysis.

Contribution

It introduces a Wigner function for rebits, proves a discrete Hudson's theorem, and links contextuality and negativity to computational universality in rebit-based quantum computing.

Findings

Wigner function negativity correlates with computational power.

Contextuality witnesses are effective for rebit states.

The framework extends to state-independent contextuality scenarios.

Abstract

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. We introduce contextuality witnesses for rebit states, and discuss the compatibility of our result with state-independent contextuality.