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  • Open Access

Tropical Contraction of Tensor Networks as a Bell Inequality Optimization Toolset

Mengyao Hu* and Jordi Tura†

  • Instituut-Lorentz, Universiteit Leiden, 2333 CA Leiden, The Netherlands and ⟨aQaL⟩ Applied Quantum Algorithms Leiden, Leiden, The Netherlands

  • *Contact author: mengyao@lorentz.leidenuniv.nl
  • †Contact author: tura@lorentz.leidenuniv.nl
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Phys. Rev. Lett. 136, 100202 – Published 12 March, 2026

DOI: https://doi.org/10.1103/r7s7-c7y2

Abstract

We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is replaced by the arithmetic addition. We illustrate our method with paradigmatic examples both in the multipartite scenario and the bipartite scenario with multiple outcomes. We showcase how the method extends into the thermodynamic limit for some translationally invariant systems and establish a connection between the notions of tropical eigenvalue and the classical bound per particle as a fixed point of a tropical renormalization procedure.

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See Also

Characterizing translation-invariant Bell inequalities using tropical algebra and graph polytopes

Mengyao Hu, Eloïc Vallée, Tim Seynnaeve, Patrick Emonts, Fatemeh Mohammadi, and Jordi Tura
Phys. Rev. A 113, 032421 (2026)

Article Text

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Phys. Rev. Lett. 136, 100202– Published 12 March, 2026
  • Received 28 October 2025
  • Revised 6 January 2026
  • Accepted 9 January 2026
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