Quantum Violations of CHSH-3 Inequality via Tensor Product Hilbert Spaces — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The CHSH-3 inequality extends the standard CHSH framework to three measurement settings per party, with quantum violations computable via semidefinite programming; the Hilbert space structure underpinning these violations is the tensor product of local Hilbert spaces, with singular values of the correlation matrix determining maximal violation bounds. | MATH: Standard CHSH: S = ⟨ AB ⟩ + ⟨ AB' ⟩ + ⟨ A'B ⟩ − ⟨ A'B' ⟩ ≤ 2 (local), Squantum ≤ 2√2 ≈ 2.828. CHSH-3 generalizes to three settings per party, with the quantum bound given by the maximal singular value of the correlation tensor Tij = ⟨ Ai ⊗ Bj ⟩, i.e., |T|∞ ≤ √3 for the specific CHSH-3 form (Tsirelson-type bound). The Hilbert space is ℋA ⊗ ℋB, and the singular value decomposition of the 3 × 3 correlation matrix yields singular values \(\sigma_1 \geq \si
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026quantum,
title = {{Quantum Violations of CHSH-3 Inequality via Tensor Product Hilbert Spaces — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23431333},
url = {https://zenodo.org/records/23431333},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Violations of CHSH-3 Inequality via Tensor Product Hilbert Spaces — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/17
PB - Zenodo
DO - 10.5281/zenodo.23431333
UR - https://zenodo.org/records/23431333
AB - FINDING: The CHSH-3 inequality extends the standard CHSH framework to three measurement settings per party, with quantum violations computable via semidefinite programming; the Hilbert space structure underpinning these violations is the tensor product of local Hilbert spaces, with singular values of the correlation matrix determining maximal violation bounds. | MATH: Standard CHSH: S = ⟨ AB ⟩ + ⟨ AB' ⟩ + ⟨ A'B ⟩ − ⟨ A'B' ⟩ ≤ 2 (local), S_quantum ≤ 2√2 ≈ 2.828. CHSH-3 generalizes to three settings per party, with the quantum bound given by the maximal singular value of the correlation tensor T_ij = ⟨ A_i ⊗ B_j ⟩, i.e., |T|_∞ ≤ √3 for the specific CHSH-3 form (Tsirelson-type bound). The Hilbert space is ℋ_A ⊗ ℋ_B, and the singular value decomposition of the 3 × 3 correlation matrix yields singular values \(\sigma_1 \geq \si Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -