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PreprintCC BY 4.0arXiv

All Bell inequalities with a quantum advantage in the minimal scenario are self-testing

  • Mu-En Liu
  • Andrea Zingarofalo
  • Victor Barizien
  • Jean-Daniel Bancal
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Abstract

In the minimal Bell scenario, all extremal quantum correlations are known, but the Tsirelson inequalities that delimit the quantum set remain poorly understood. We study which correlations can maximize a given Tsirelson inequality, and conversely, which inequalities are maximized by a given correlation. We show that every Tsirelson inequality with quantum advantage is maximized by a single, extremal correlation, and thus self-tests the corresponding realization. This characterizes all self-tests based on linear Bell inequalities in this scenario. We also show that at most a two-dimensional family of inequalities can be maximized by a nonlocal extremal correlation. We identify these as polygons for a family of correlations realized by qubit states of arbitrary entanglement. This allows us to deduce that the quantum set is not self-dual.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026bell,
  title = {{All Bell inequalities with a quantum advantage in the minimal scenario are self-testing}},
  author = {Mu-En Liu and Andrea Zingarofalo and Victor Barizien and Jean-Daniel Bancal},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06997},
  eprint = {2611.06997},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06997},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - All Bell inequalities with a quantum advantage in the minimal scenario are self-testing
AU  - Mu-En Liu
AU  - Andrea Zingarofalo
AU  - Victor Barizien
AU  - Jean-Daniel Bancal
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06997
UR  - https://arxiv.org/abs/2611.06997
AB  - In the minimal Bell scenario, all extremal quantum correlations are known, but the Tsirelson inequalities that delimit the quantum set remain poorly understood. We study which correlations can maximize a given Tsirelson inequality, and conversely, which inequalities are maximized by a given correlation. We show that every Tsirelson inequality with quantum advantage is maximized by a single, extremal correlation, and thus self-tests the corresponding realization. This characterizes all self-tests based on linear Bell inequalities in this scenario. We also show that at most a two-dimensional family of inequalities can be maximized by a nonlocal extremal correlation. We identify these as polygons for a family of correlations realized by qubit states of arbitrary entanglement. This allows us to deduce that the quantum set is not self-dual.
ER  -