Genuinely multipoint temporal quantum correlations and universal measurement-based quantum computing

• Main Authors: Markiewicz, Marcin, Przysiężna, Anna, Brierley, Stephen, Paterek, Tomasz
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Physics
• Online Access: https://hdl.handle.net/10356/104875; http://hdl.handle.net/10220/20305
• Institution: Nanyang Technological University

We introduce a constructive procedure that maps all spatial correlations of a broad class of d -level states of N parties into temporal correlations between general d -outcome quantum measurements performed on a single d -level system. This allows us to present temporal phenomena analogous to genuinely multipartite nonlocal phenomena, such as Greenberger-Horne-Zeilinger correlations, which do not exist if only projective measurements on a single qubit are considered. The map is applied to certain lattice systems in order to replace one spatial dimension with a temporal one, without affecting measured correlations. We use this map to show how repeated application of a one-dimensional (1D) cluster gate leads to universal one-way quantum computing when supplemented with general two-outcome quantum measurements. In this way, we recover a temporal version of measurement-based quantum computing performed on a sequentially recreated 1D cluster.