Density cubes and higher-order interference theories

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 a...

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Main Authors: Dakić, B, Paterek, Tomasz, Brukner, Č
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2014
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Online Access:https://hdl.handle.net/10356/102810
http://hdl.handle.net/10220/19126
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1028102023-02-28T19:42:46Z Density cubes and higher-order interference theories Dakić, B Paterek, Tomasz Brukner, Č School of Physical and Mathematical Sciences DRNTU::Science::Physics::Atomic physics::Quantum theory 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. Published version 2014-04-04T07:48:20Z 2019-12-06T21:00:36Z 2014-04-04T07:48:20Z 2019-12-06T21:00:36Z 2014 2014 Journal Article Dakić, B., Paterek, T., & Brukner, Č. (2014). Density cubes and higher-order interference theories. New Journal of Physics, 16(2), 023028-. 1367-2630 https://hdl.handle.net/10356/102810 http://hdl.handle.net/10220/19126 10.1088/1367-2630/16/2/023028 en 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. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Physics::Atomic physics::Quantum theory
spellingShingle DRNTU::Science::Physics::Atomic physics::Quantum theory
Dakić, B
Paterek, Tomasz
Brukner, Č
Density cubes and higher-order interference theories
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Dakić, B
Paterek, Tomasz
Brukner, Č
format Article
author Dakić, B
Paterek, Tomasz
Brukner, Č
author_sort Dakić, B
title Density cubes and higher-order interference theories
title_short Density cubes and higher-order interference theories
title_full Density cubes and higher-order interference theories
title_fullStr Density cubes and higher-order interference theories
title_full_unstemmed Density cubes and higher-order interference theories
title_sort density cubes and higher-order interference theories
publishDate 2014
url https://hdl.handle.net/10356/102810
http://hdl.handle.net/10220/19126
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