Density cubes and higher-order interference theories

Author(s): B. Dakić, T. Paterek, Č. Brukner

Journal: New Journal of Physics

Volume: 16

Page(s): 023028

Year: 2014

DOI Number: http://dx.doi.org/10.1088/1367-2630/16/2/023028

Link: Link to publication

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.

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