Density cubes and higher-order interference theories
Date of Issue2014
School of Physical and Mathematical Sciences
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.
DRNTU::Science::Physics::Atomic physics::Quantum theory
New Journal of Physics
© 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. This paper was published in New Journal of Physics and is made available as an electronic reprint (preprint) with permission of IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. The paper can be found at the following official DOI: [http://dx.doi.org/10.1088/1367-2630/16/2/023028]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.