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