bibkey: hanotelloubenets2025chshspinone
authors: Louis Hanotel and Elena R. Loubenets
year: 2025
title: "Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits"
doi: 10.1088/1402-4896/adcc66
url: "https://arxiv.org/abs/2503.05172v2"
claim: "For two spin-s qudits measured by the spin projections S_r=r·S with unit vectors r, the CHSH inequality has local bound 2s^2; the paper finds analytically and numerically that spin-1 measurements violate it for no tested two-qutrit state, conjectures nonviolation for every two-qutrit state, and states that whether the CHSH inequality is violated under high-spin s≥1 measurements is still open."
strata_touched:
  - D5/S3/QuantumBounds/HighSpinCHSHNonviolation
license: citation-only
triage: anchor

Hanotel and Loubenets, Nonviolation of the CHSH inequality under local spin-1 measurements on two spin qutrits

L. Hanotel and E. R. Loubenets, Phys. Scr. 100(5), 055115 (2025); arXiv:2503.05172v2. Quotations are from the v2 TeX source. The spin observables and the CHSH setting are those of the companion paper E. R. Loubenets and L. Hanotel, “High-spin measurements in an arbitrary two-qudit state”, J. Phys. A: Math. Theor. 58(26), 265304 (2025), DOI 10.1088/1751-8121/ade4e8, arXiv:2412.03470v2.

For a spin-$s$ qudit of dimension $d=2s+1$, Alice and Bob measure spin projections $S_r=r\cdot S$ with unit vectors $r\in {\mathbb{R}}^3$; the CHSH operator is $S_{a_1}\otimes S_{b_1}+S_{a_1}\otimes S_{b_2}+S_{a_2}\otimes S_{b_1}-S_{a_2}\otimes S_{b_2}$, and since spin-$s$ observables have eigenvalues in $[-s,s]$ the local-hidden-variable bound is $2s^2$. The paper states:

However, up to the moment the problem whether or not the CHSH inequality is violated under Alice and Bob high spin $s\ge 1$ measurements is still open – though specifically this Bell inequality has been used for proving [1, Lou.Kuz.Han:24] nonlocality of every pure nonseparable two-qudit state.

It then treats spin 1 and conjectures that no two-qutrit state violates the CHSH inequality under local spin-1 measurements.

Verified locator

Source: https://arxiv.org/abs/2503.05172v2

• DOI: https://doi.org/10.1088/1402-4896/adcc66 (Physica Scripta 100(5), 055115, 2025; title, authors, journal, volume, issue and article number from Crossref).
• URL: https://arxiv.org/abs/2503.05172v2. The e-print member Final_Revision_Hanotel_Loubenets.tex has 1200 lines and md5 1ee1518c0b95e586819f229b14c4e079. Locations:
  • the CHSH expectation and operator (0.1), l. 108–115;
  • the open problem for high spin $s\ge 1$, l. 201;
  • the spin-1 conjecture, l. 209 and 902–918.
• Companion paper: https://arxiv.org/abs/2412.03470v2, member Revision_Loubenets_Hanotel.tex (1011 lines, md5 589158d190960a369b504a4aa9566d18): the spin projections and the matrices $S_1,S_2,S_3$, l. 210–237; the CHSH operator for spin observables, l. 253–261; the bound $2s^2$, l. 348–356.