Evaluation of Estimation Precision in Test of Bell-Type Correlations

Timothy C. Ralph, William J. Munro, Rodney Polkinghorne

Dongkeun Lee, Wonmin Son

For the identification of non-trivial quantum phase, we exploit a Bell-type correlation that is applied to the one-dimensional spin-1 XXZ chain. It is found that our generalization of bipartite Bell correlation can take a decomposed form of transverse spin correlation together with high-order terms. The formulation of the density-matrix renormalisation group is utilized to obtain the ground state of a given Hamiltonian with non-trivial phase. Subsequently Bell-type correlation is evaluated through the analysis of the matrix product state. Diverse classes of quantum phase transitions in the spin-1 model are identified precisely through the evaluation of the first and the second moments of the generalized Bell correlations. The role of high-order terms in the criticality has been identified and their physical implications for the quantum phase have been revealed.

G. F. Bertsch, J. Borysowicz

Roberto Locatelli

QRAFT-RA (Quadrature-based Reproducible Action-Structured Framework with Regularized Action) is a deterministic contextual variational framework for generating and verifying non-classical correlations through a fully reproducible computational pipeline. The framework combines: • a contextual action landscape on a compact latent domain• a Gibbs-type contextual distribution controlled by an inverse temperature parameter• an analytic noise-aware measurement map• deterministic quadrature evaluation of correlators and Bell-type functionals A complete deterministic verification hierarchy (V1–V17) is reported, including convergence tests, adversarial optimization under operational no-signaling constraints, industrial correlator validation (V14), and Titan-scale statistical stress testing (V15). In the General-MD regime the framework deterministically generates super-Tsirelson correlations: CHSH ≈ 3.576310390010 while maintaining operational no-signaling at machine precision: SIG ≈ 10⁻¹⁶. The work is presented as a deterministic mathematical and computational archetype for exploring contextual correlation structures and reproducible simulation pipelines. Related patent application:PCT/IB2026/050200 (QRAFT-RA-PCT-2026-01).

Arthur I. Fine

Koji Nagata, Masato Koashi, Nobuyuki Imoto

We derive tight quadratic inequalities for all kinds of hybrid separable-inseparable n-particle density operators on an arbitrary dimensional space. This methodology enables us to derive a tight quadratic inequality as tests for full n-partite entanglement in various Bell-type correlation experiments on the systems that may not be identified as a collection of qubits, e.g., those involving photons measured by incomplete detectors. It is also proved that when the two measured observables are assumed to precisely anticommute, a stronger quadratic inequality can be used as a witness of full n-partite entanglement.