Density cubes and higher-order interference theories

• Main Authors: Dakić, B, Paterek, Tomasz, Brukner, Č
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Physics::Atomic physics::Quantum theory
• Online Access: https://hdl.handle.net/10356/102810; http://hdl.handle.net/10220/19126
• Institution: Nanyang Technological University

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.