Tailored two-photon correlation and fair-sampling: a cautionary tale

Romero, J., Giovannini, D., Tasca, D.S., Barnett, S.M. and Padgett, M.J. (2013) Tailored two-photon correlation and fair-sampling: a cautionary tale. New Journal of Physics, 15, 083047. (doi: 10.1088/1367-2630/15/8/083047)

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We demonstrate an experimental test of the Clauser–Horne– Shimony–Holt (CHSH) Bell inequality which seemingly exhibits correlations beyond the limits imposed by quantum mechanics. Inspired by the idea of Fourier synthesis, we design analysers that measure specific superpositions of orbital angular momentum (OAM) states, such that when one analyser is rotated with respect to the other, the resulting coincidence curves are similar to a square-wave. Calculating the CHSH Bell parameter, S, from these curves result to values beyond the Tsirelson bound of $S_{\mathrm {QM}}=2\sqrt {2}$ . We obtain S = 3.99 ± 0.02, implying almost perfect nonlocal Popescu–Rohrlich correlations. The 'super-quantum' values of S is only possible in our experiment because our experiment, subtly, does not comply with fair-sampling. The way our Bell test fails fair-sampling is not immediately obvious and requires knowledge of the states being measured. Our experiment highlights the caution needed in Bell-type experiments based on measurements within high-dimensional state spaces such as that of OAM, especially in the advent of device-independent quantum protocols.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Padgett, Professor Miles and Barnett, Professor Stephen and Tasca, Dr Daniel and Giovannini, Dr Daniel and Romero, Dr Mary
Authors: Romero, J., Giovannini, D., Tasca, D.S., Barnett, S.M., and Padgett, M.J.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:New Journal of Physics
Publisher:Institute of Physics Publishing Ltd.
ISSN (Online):1367-2630
Copyright Holders:Copyright © 2013 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft
First Published:First published in New Journal of Physics 15(083047)
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
549871Challenges in Orbital Angular MomentumMiles PadgettEngineering & Physical Sciences Research Council (EPSRC)EP/I012451/1P&A - PHYSICS & ASTRONOMY