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    Quantum Contextuality with Stabilizer States

    Howard, Mark and Brennan, Eoin and Vala, Jiri (2013) Quantum Contextuality with Stabilizer States. Entropy, 15. pp. 2340-2362. ISSN 1099-4300

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    The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error correcting codes—stabilizer codes—are built using Pauli operators. The eigenstates of these operators—stabilizer states—display a structure (e.g., mutual orthogonality relationships) that has made them useful in examples of multi-qubit non-locality and contextuality. Here, we apply the graph-theoretical contextuality formalism of Cabello, Severini and Winter to sets of stabilizer states, with particular attention to the effect of generalizing two-level qubit systems to odd prime d-level qudit systems. While state-independent contextuality using two-qubit states does not generalize to qudits, we show explicitly how state-dependent contextuality associated with a Bell inequality does generalize. Along the way we note various structural properties of stabilizer states, with respect to their orthogonality relationships, which may be of independent interest.

    Item Type: Article
    Additional Information: The definitive version of this article is available at Howard, M.; Brennan, E.; Vala, J. Quantum Contextuality with Stabilizer States. Entropy 2013, 15, 2340-2362. M.H. was financially supported by the Irish Research Council (IRC) as part of the Empower Fellowship program. J.V. acknowledges support from Science Foundation Ireland under the Principal Investigator Award No. 10/IN.1/I3013. We thank Joseph Emerson for helpful comments on a previous version of this manuscript. Published under a Creative Commons Attribution License
    Keywords: contextuality; stabilizer; non-locality;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 5565
    Identification Number:
    Depositing User: Dr. Jiri Vala
    Date Deposited: 19 Nov 2014 16:00
    Journal or Publication Title: Entropy
    Publisher: MDPI
    Refereed: Yes
    Funders: Irish Research Council, Science Foundation Ireland
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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