Year: 2026
Type: article
Abstract: We propose an information-theoretic framework for quantifying Kochen–Specker contextuality. Two complementary measures are introduced: the mutual information energy, a state-independent quantity inspired by Onicescu’s information energy that captures the geometric overlap between joint eigenspaces within a context; and an operational measure based on commutator expectation values that reflects contextual behavior at the level of measurement outcomes. We establish a hierarchy of bounds connecting these measures to the Robertson uncertainty relation, including spectral, purity-corrected, and operator norm estimates. The framework is applied to the Klyachko–Can–Binicioğlu–Shumovsky (KCBS) scenario for spin-1 systems, where all quantities admit closed-form expressions. The Majorana-stellar representation furnishes a common geometric platform on which both the operational measure and the uncertainty products can be analyzed. For spin-1, this representation yields a three-dimensional Euclidean-like visualization of the Hilbert space in which states lying on a plane exhibit maximum uncertainty for the observable along the perpendicular direction; simultaneous optimization across all KCBS contexts singles out a unique state on the symmetry axis. Notably, states achieving the optimal sum of uncertainty products exhibit vanishing operational contextuality, while states with substantial operational contextuality satisfy a nontrivial Robertson bound—the two extremes are realized by distinct quantum states.
Authors: A C Günhan, Z Gedik
Institutions: Mersin Üniversitesi, Sabancı Üniversitesi
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W7115594478