Almost Quantum Correlations are Inconsistent with Specker's Principle

Tomáš Gonda; Ravi Kunjwal; David Schmid; Elie Wolfe; Ana Belén Sainz

doi:10.22331/q-2018-08-27-87

Almost Quantum Correlations are Inconsistent with Specker’s Principle

Tomáš Gonda^1,2, Ravi Kunjwal¹, David Schmid^1,2, Elie Wolfe¹, and Ana Belén Sainz¹

¹Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L 2Y5
²Dept. of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

Published:	2018-08-27, volume 2, page 87
Eprint:	arXiv:1712.01225v2
Doi:	https://doi.org/10.22331/q-2018-08-27-87
Citation:	Quantum 2, 87 (2018).

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Abstract

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability ($\href{https://vimeo.com/52923835}{vimeo.com/52923835}$). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations. Here we show that, contrary to the popular belief, Specker's principle cannot be satisfied in any theory that yields almost quantum correlations.

► BibTeX data

@article{Gonda2018almostquantum,
  doi = {10.22331/q-2018-08-27-87},
  url = {https://doi.org/10.22331/q-2018-08-27-87},
  title = {Almost {Q}uantum {C}orrelations are {I}nconsistent with {S}pecker's {P}rinciple},
  author = {Gonda, Tom{\'{a}}{\v{s}} and Kunjwal, Ravi and Schmid, David and Wolfe, Elie and Sainz, Ana Bel{\'{e}}n},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {87},
  month = aug,
  year = {2018}
}

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[3] Ravi Kunjwal, "Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem", Quantum 4, 219 (2020).

[4] David Schmid, John H. Selby, Vinicius P. Rossi, Roberto D. Baldijão, and Ana Belén Sainz, "Shadows and subsystems of generalized probabilistic theories: when tomographic incompleteness is not a loophole for contextuality proofs", Quantum 9, 1880 (2025).

[5] Nikola Andrejic and Ravi Kunjwal, "Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery", Physical Review Research 2 4, 043147 (2020).

[6] Yujie Zhang, David Schmid, Yìlè Yīng, and Robert W. Spekkens, "Reassessing the Boundary between Classical and Nonclassical for Individual Quantum Processes", Physical Review X 16 2, 021050 (2026).

[7] Ravi Kunjwal, "Beyond the Cabello-Severini-Winter framework: Making sense of contextuality without sharpness of measurements", Quantum 3, 184 (2019).

[8] Pei-Sheng Lin, Tamás Vértesi, and Yeong-Cherng Liang, "Naturally restricted subsets of nonsignaling correlations: typicality and convergence", Quantum 6, 765 (2022).

[9] Sacha Huriot-Tattegrain and Mehdi Mhalla, "Contextuality and Expressivity of Non-locality", Electronic Proceedings in Theoretical Computer Science 340, 160 (2021).

[10] David Schmid, Roberto D. Baldijão, Yìlè Yīng, Rafael Wagner, and John H. Selby, "Kirkwood-Dirac representations beyond quantum states and their relation to noncontextuality", Physical Review A 110 5, 052206 (2024).

[11] Sumit Mukherjee and A K Pan, "Constrained measurement incompatibility from generalised contextuality of steered preparation", New Journal of Physics 26 12, 123014 (2024).

[12] Ravishankar Ramanathan, "Violation of all two-party facet Bell inequalities by almost-quantum correlations", Physical Review Research 3 3, 033100 (2021).

[13] José Nogueira, Carlos Vieira, and Marcelo Terra Cunha, "Unexpected consequences of postquantum theories in the graph-theoretical approach to correlations", Physical Review A 111 5, 052418 (2025).

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[15] David Schmid, Haoxing Du, Maryam Mudassar, Ghi Coulter-de Wit, Denis Rosset, and Matty J. Hoban, "Postquantum common-cause channels: the resource theory of local operations and shared entanglement", Quantum 5, 419 (2021).

[16] Shiv Akshar Yadavalli, Nikola Andrejic, and Ravi Kunjwal, "Qualitative equivalence between incompatibility and Bell nonlocality", Physical Review A 110 6, L060201 (2024).

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