Wigner function negativity and contextuality in quantum computation on rebits

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.

18 + 4 pages

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Cited by in corpus (8)

• Application of a resource theory for magic states to fault-tolerant quantum computing
• Necessary and sufficient condition for quantum state-independent contextuality
• Locality-Preserving Logical Operators in Topological Stabiliser Codes
• Discrete Wigner Formalism for Qubits and Non-Contextuality of Clifford Gates on Qubit Stabilizer States
• Contextuality in phase space
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
• Experimental demonstration of the connection between quantum contextuality and graph theory
• On the tightness of correlation inequalities with no quantum violation