A complete characterization of all-versus-nothing arguments for stabilizer states

作者：Abramsky Samson^*; Barbosa Rui Soares; Caru Giovanni; Perdrix Simon

来源：Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2017, 375(2106): 20160385.

DOI：10.1098/rsta.2016.0385

• contextuality
• all-versus-nothing arguments
• stabilizer states
• graph states

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 Z(2) 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'.

• 出版日期2017-11-13