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Equivalence between contextuality and negativity of the Wigner function for qudits

Delfosse, Nicolas and Okay, Cihan and Bermejo-Vega, Juan and Browne, Dan E. and Raussendorf, Robert (2017) Equivalence between contextuality and negativity of the Wigner function for qudits. New Journal of Physics, 19 (12). Art. No. 123024. ISSN 1367-2630. https://resolver.caltech.edu/CaltechAUTHORS:20180102-134007465

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Abstract

Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality for quantum systems, negativity of the Wigner function and contextuality for Pauli measurements. We prove that these two notions are equivalent for multi-qudit systems with odd local dimension. For a single qudit, the equivalence breaks down. We show that there exist single qudit states that admit a non-contextual hidden variable model description and whose Wigner functions are negative.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1367-2630/aa8fe3DOIArticle
http://iopscience.iop.org/article/10.1088/1367-2630/aa8fe3/metaPublisherArticle
https://arxiv.org/abs/1610.07093arXivDiscussion Paper
ORCID:
AuthorORCID
Delfosse, Nicolas0000-0002-3949-981X
Additional Information:© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 27 April 2017. Accepted 29 September 2017. Published 8 December 2017. ND acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-2644). CO acknowledges funding from NSERC. JBV acknowledges funding from AQuS. RR is supported by NSERC and Cifar. RR thanks Ana Belén Sainz for discussions. ND thanks Kamil Korzekwa for his comments on a preliminary version of this work. DB acknowledges funding provided by EPSRC Centre for Doctoral Training in Delivering Quantum Technologies. DB and JBV thank the Perimeter Institute for its hospitality and during the conference, 'Contextuality: Conceptual Issues, Operational Signatures, and Applications'.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Universität HeidelbergUNSPECIFIED
Subject Keywords:discrete Wigner functions, contextuality, hidden variable model, quantum computing
Issue or Number:12
Record Number:CaltechAUTHORS:20180102-134007465
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180102-134007465
Official Citation:Nicolas Delfosse et al 2017 New J. Phys. 19 123024
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84033
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:02 Jan 2018 22:20
Last Modified:03 Oct 2019 19:13

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