Abramsky Samson, Barbosa Rui Soares, Carù Giovanni, Perdrix Simon
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK
Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
Philos Trans A Math Phys Eng Sci. 2017 Nov 13;375(2106). doi: 10.1098/rsta.2016.0385.
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 -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 [Formula: see text] on -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'.
量子基础中一类重要的上下文相关性论证是全有或全无（AvN）证明，它推广了最初由默明提出的一种构造。我们给出了AvN论证的一般形式，并对所有源于稳定器态的此类论证进行了完整刻画。我们表明，对于一个(n)量子比特稳定器态的每一个AvN论证都可以简化为一个针对与三方格林伯格 - 霍恩 - 泽林格态局部克利福德等价的三量子比特态的AvN证明。这是通过对AvN论证的组合刻画，即AvN三元定理来实现的，其证明利用了图态理论。这一结果使得能够开发一种计算方法来生成关于(n)量子比特稳定器态的所有AvN论证。我们还对稳定器形式体系及其与逻辑的联系给出了新的见解。本文是主题为“第二次量子革命：基础问题”的特刊的一部分。
