### Abstract

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 . 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.*

Language | English |
---|---|

Article number | 083047 |

Number of pages | 11 |

Journal | New Journal of Physics |

Volume | 15 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2013 |

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### Keywords

- Clauser–Horne– Shimony–Holt (CHSH)
- Fourier synthesis
- orbital angular momentum (OAM) states
- CHSH Bell experiments

### Cite this

*New Journal of Physics*,

*15*(8), [083047]. https://doi.org/10.1088/1367-2630/15/8/083047

}

*New Journal of Physics*, vol. 15, no. 8, 083047. https://doi.org/10.1088/1367-2630/15/8/083047

**Tailored two-photon correlation and fair-sampling : a cautionary tale.** / Romero, J; Giovannini, D; Tasca, D S; Barnett, S M; Padgett, M J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Tailored two-photon correlation and fair-sampling

T2 - New Journal of Physics

AU - Romero, J

AU - Giovannini, D

AU - Tasca, D S

AU - Barnett, S M

AU - Padgett, M J

PY - 2013

Y1 - 2013

N2 - 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 . 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.

AB - 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 . 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.

KW - Clauser–Horne– Shimony–Holt (CHSH)

KW - Fourier synthesis

KW - orbital angular momentum (OAM) states

KW - CHSH Bell experiments

UR - http://stacks.iop.org/1367-2630/15/i=8/a=083047

U2 - 10.1088/1367-2630/15/8/083047

DO - 10.1088/1367-2630/15/8/083047

M3 - Article

VL - 15

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 8

M1 - 083047

ER -