Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities

Soumyabrata Hazra; Debashis Saha; Anubhav Chaturvedi; Subhankar Bera; A. S. Majumdar

doi:10.22331/q-2026-03-09-2015

Efficient Computation of Generalized Noncontextual Polytopes and Quantum violation of their Facet Inequalities

Soumyabrata Hazra¹, Debashis Saha^2,3, Anubhav Chaturvedi^4,5, Subhankar Bera^6,7, and A. S. Majumdar⁶

¹International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
²School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
³Department of Physics, School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Odisha 752050, India
⁴Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
⁵International Centre for Theory of Quantum Technologies (ICTQT), University of Gdańsk, 80-308 Gdańsk, Poland
⁶S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
⁷Department of Physics and Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan

Published:	2026-03-09, volume 10, page 2015
Editor:	Paul Skrzypczyk
Eprint:	arXiv:2406.09111v3
Doi:	https://doi.org/10.22331/q-2026-03-09-2015
Citation:	Quantum 10, 2015 (2026).

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Abstract

Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the noncontextual polytope while ensuring that the dimension of the polytope associated with the preparations remains constant regardless of the number of measurements and their outcome size. The facet inequalities of the noncontextual polytope can thus be obtained in a computationally efficient manner. We illustrate the efficacy of our methodology through several distinct contextuality scenarios. Our investigation uncovers several hitherto unexplored noncontextuality inequalities and demonstrates applications of quantum contextual correlations in certification of non-projective measurements, witnessing the dimension of quantum systems, and randomness certification.

► BibTeX data

@article{Hazra2026efficient,
  doi = {10.22331/q-2026-03-09-2015},
  url = {https://doi.org/10.22331/q-2026-03-09-2015},
  title = {Efficient {C}omputation of {G}eneralized {N}oncontextual {P}olytopes and {Q}uantum violation of their {F}acet {I}nequalities},
  author = {Hazra, Soumyabrata and Saha, Debashis and Chaturvedi, Anubhav and Bera, Subhankar and Majumdar, A. S.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2015},
  month = mar,
  year = {2026}
}

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Cited by

[1] Anubhav Chaturvedi, Marcin Pawłowski, and Debashis Saha, "Epistemic incompleteness of quantum theory", Physical Review A 113 4, 042445 (2026).

[2] Ankush Pandit, Soumyabrata Hazra, Satyaki Manna, Anubhav Chaturvedi, and Debashis Saha, "Limits of classical correlations and quantum advantages under (anti-)distinguishability constraints in multipartite communication", Physical Review A 113 3, 032433 (2026).

[3] Rafael Wagner, "Coherence and contextuality as quantum resources", arXiv:2511.16785, (2025).

[4] Ankush Pandit, "Quantum advantages in multiparty communication", arXiv:2512.05538, (2025).

[5] Nilaj Saha, Sumit Mukherjee, and Dipankar Home, "Intraparticle entanglement-based Random Access Code protocols: Contextuality-enabled quantum advantage and implications", arXiv:2605.13350, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-19 21:08:25) and SAO/NASA ADS (last updated successfully 2026-08-19 21:08:26). The list may be incomplete as not all publishers provide suitable and complete citation data.

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