Bipartite polygon models: entanglement classes and their nonlocal behaviour

Mayalakshmi Kolangatt; Thigazholi Muruganandan; Sahil Gopalkrishna Naik; Tamal Guha; Manik Banik; Sutapa Saha

doi:10.22331/q-2025-01-20-1599

Bipartite polygon models: entanglement classes and their nonlocal behaviour

Mayalakshmi Kolangatt¹, Thigazholi Muruganandan¹, Sahil Gopalkrishna Naik², Tamal Guha³, Manik Banik², and Sutapa Saha^4,5

¹School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India.
²Department of Physics of Complex Systems, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India.
³Department of Computer Science, The University of Hong Kong, Pokfulam road 999077, Hong Kong.
⁴Department of Astrophysics and High Energy Physics, S.N. Bose National Center for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India.
⁵Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019, India.

Published:	2025-01-20, volume 9, page 1599
Editor:	Ion Nechita
Eprint:	arXiv:2205.05415v5
Doi:	https://doi.org/10.22331/q-2025-01-20-1599
Citation:	Quantum 9, 1599 (2025).

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Abstract

Hardy's argument constitutes an elegantly logical test for identifying nonlocal features of multipartite correlations. In this paper, we investigate Hardy's nonlocal behavior within a broad class of operational theories, including the qubit state space as a specific case. Specifically, we begin by examining a wider range of operational models with state space descriptions in the form of regular polygons. First, we present a systematic method to characterize the possible forms of entangled states within bipartite compositions of these models. Then, through explicit examples, we identify the classes of entangled states that exhibit Hardy-type nonlocality. Remarkably, our findings highlight a closer analogy between odd polygon models and the qubit state space in terms of their bipartite Hardy nonlocal behavior compared to even-sided polygons. Furthermore, we demonstrate that the emergence of mixed-state Hardy nonlocality in any operational model is determined by a specific symmetry inherent in its dynamic description. Finally, our results uncover an unexplored class of almost-quantum correlations that can be associated with an explicit operational model.

Featured image: Hardy's Nonlocality & Preparation-measurement Reciprocity

Popular summary

Among various formulations of nonlocality tests, one of the most elegant demonstrations
of quantum nonlocality comes without inequalities, as proposed by Lucian Hardy. Unlike
the celebrated Bell-CHSH test, in the two-qubit scenario, this signature of nonlocality is
uniquely exhibited by pure entangled states. But what is so special about the topology of
the qubit state space? Why not Hardy’s nonlocal argument is robust even with a vanishing
presence of product qubit noises?
This work highlights a key feature of single quanta: the one-to-one correspondence be-
tween their preparation and measurement devices, which leads to such an extreme noise
sensitivity of Hardy’s nonlocal phenomenon in bipartite systems. Moreover, the result ex-
tends to a broader class of operational probabilistic models, encompassing both classical
and quantum theories. This generalization offers theory-independent predictive capability
for identifying noise-robust Hardy-type nonlocal signatures in any operational theory with
exactly two simultaneously distinguishable pure preparations.

► BibTeX data

@article{Kolangatt2025bipartitepolygon,
  doi = {10.22331/q-2025-01-20-1599},
  url = {https://doi.org/10.22331/q-2025-01-20-1599},
  title = {Bipartite polygon models: entanglement classes and their nonlocal behaviour},
  author = {Kolangatt, Mayalakshmi and Muruganandan, Thigazholi and Naik, Sahil Gopalkrishna and Guha, Tamal and Banik, Manik and Saha, Sutapa},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1599},
  month = jan,
  year = {2025}
}

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Cited by

[1] Martin Plávala, "General probabilistic theories: An introduction", Physics Reports 1033, 1 (2023).

[2] Samrat Sen, Edwin Peter Lobo, Ram Krishna Patra, Sahil Gopalkrishna Naik, Anandamay Das Bhowmik, Mir Alimuddin, and Manik Banik, "Timelike correlations and quantum tensor product structure", Physical Review A 106 6, 062406 (2022).

[3] Ryo Takakura, "Optimal CHSH values for regular polygon theories in generalized probabilistic theories", Journal of Physics A Mathematical General 57 37, 375305 (2024).

[4] Anna Steffinlongo, Nicola D'Alessandro, and Martin J. Renner, "Almost all pure entangled states enable unbounded nonlocality sharing", arXiv:2607.24700, (2026).

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