Certified exact identification of the I3322 quantum value
quant-ph
Submitted: 2026-08-31
Updated: 2026-08-31
Comments: 16 pages; computer-assisted proof; complete verification artifact at DOI 10.5281/zenodo.22160086
License: http://creativecommons.org/licenses/by/4.0/
The gist: We determine the quantum value of the three-setting, two-outcome Bell functional I3322.
Terminology
Abstract
We determine the quantum value of the three-setting, two-outcome Bell functional I3322. The value is the unique intersection q of an analytic A-high stable curve of the exact Jacobi characteristic map with a central reverser curve. A computer-assisted proof isolates this intersection in a rational interval of width 10-55, beginning 0.2508753845139765356173366109459512989013219739714764755. We prove that the supremum over finite-dimensional tensor-product strategies, the unrestricted spatial value and the commuting-operator value all equal q. No finite-dimensional strategy attains the value, whereas a normal infinite-dimensional spatial strategy and a commuting GNS strategy do. The proof combines an exact Bellman/path variational reduction, extraction of a positive bilateral calibrated Jacobi fibre from a maximizing weak-star state, a reflected-fibre central-incidence theorem and interval certificates for the unique stable/central intersection. A separate operator-positive three-remainder decomposition gives the commuting upper bound. The complete verification record is archived at DOI 10.5281/zenodo.22160086.
Sources
- A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
- Maximal violation of the I3322 inequality using infinite dimensional quantum systems
- Quantum value for a family of $I_{3322}$-like Bell functionals
Related papers
- Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
- Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
- Polynomial-time classical and quantum simulation of quantum impurity models
- A quasiparticle-protected superconducting qubit
- Theory of quantum-enhanced interferometry with general Markovian light sources
- A convergent hierarchy of spectral gap certificates for qubit Hamiltonians