An important class of contextuality arguments in quantum foundations are the all-versus-nothing (AvN) proofs, generalizing a construction originally due to Mermin. We present a general formulation of AvN arguments and a complete characterization of all such arguments that arise from stabilizer states. We show that every AvN argument for an n-qubit stabilizer state can be reduced to an AvN proof for a three-qubit state that is local Clifford-equivalent to the tripartite Greenberger-Horne-Zeilinger state. This is achieved through a combinatorial characterization of AvN arguments, the AvN triple theorem, whose proof makes use of the theory of graph states. This result enables the development of a computational method to generate all the AvN arguments in Z2 on n-qubit stabilizer states. We also present new insights into the stabilizer formalism and its connections with logic. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.
|Number of pages||18|
|Journal||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Early online date||2 Oct 2017|
|Publication status||Published - 13 Nov 2017|
- All-versus-nothing arguments
- Graph states
- Stabilizer states