A complete characterisation of All-versus-Nothing arguments for stabiliser states

Abstract : An important class of contextuality arguments in quantum foundations are the All-versus-Nothing (AvN) proofs, generalising a construction originally due to Mermin. We present a general formulation of All-versus-Nothing arguments, and a complete characterisation of all such arguments which arise from stabiliser states. We show that every AvN argument for an n-qubit stabiliser state can be reduced to an AvN proof for a three-qubit state which is local Clifford-equivalent to the tripartite GHZ state. This is achieved through a combinatorial characterisation 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 stabiliser states. We also present new insights into the stabiliser formalism and its connections with logic.
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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2017, Second quantum revolution: foundational questions, 375 (2106), 〈10.1098/rsta.2016.0385〉
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Contributeur : Simon Perdrix <>
Soumis le : lundi 29 mai 2017 - 15:08:58
Dernière modification le : jeudi 11 janvier 2018 - 06:21:25

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Samson Abramsky, Rui Soares Barbosa, Giovanni Carù, Simon Perdrix. A complete characterisation of All-versus-Nothing arguments for stabiliser states. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2017, Second quantum revolution: foundational questions, 375 (2106), 〈10.1098/rsta.2016.0385〉. 〈hal-01528687〉

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