Density cubes and higher-order interference theories

Author(s)
B. Dakic, T. Paterek, C. Brukner
Abstract

Can quantum theory be seen as a special case of a more general probabilistic theory, as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of interference they exhibit as proposed by Sorkin. A simple operational argument shows that the theories require higher-order tensors as a representation of physical states. For the third-order interference we derive an explicit theory of 'density cubes' and show that quantum theory, i.e. theory of density matrices, is naturally embedded in it. We derive the genuine non-quantum class of states and non-trivial dynamics for the case of a three-level system and show how one can construct the states of higher dimensions. Additionally to genuine third-order interference, the density cubes are shown to violate the Leggett-Garg inequality beyond the quantum Tsirelson bound for temporal correlations.

Organisation(s)
Quantum Optics, Quantum Nanophysics and Quantum Information
External organisation(s)
National University of Singapore (NUS), Österreichische Akademie der Wissenschaften (ÖAW), Nanyang Technological University (NTU)
Journal
New Journal of Physics
Volume
16
No. of pages
15
ISSN
1367-2630
DOI
https://doi.org/10.1088/1367-2630/16/2/023028
Publication date
02-2014
Peer reviewed
Yes
Austrian Fields of Science 2012
103025 Quantum mechanics, 103036 Theoretical physics
Keywords
Portal url
https://ucrisportal.univie.ac.at/en/publications/7ae9d539-ad6c-4a7f-80db-fae3675efd67