Contextuality under characterized loss: quantifying missing contextual information via channel-transported relative entropy
Year: 2026
Type: article
Abstract: Relative-entropy measures of contextuality quantify the statistical distance between an empirical model and the noncontextual set. We study how this established quantity changes when an experiment is observed through a characterized loss mechanism. Each attempted trial is retained in the analysis, with missed outcomes represented by context-labeled no-click symbols, and the same stochastic observation channel is applied to the target model and every noncontextual comparator. Under this common-channel transportability assumption, the data-processing inequality gives an observed-data contextual divergence that cannot exceed its complete-data value. We define the absolute contextual-information loss and its normalized ratio, the fraction of missing contextual information (FMCI). We prove general reference-set contraction, exact scaling under missing completely at random loss, a cellwise erasure sandwich, a no-exact-hiding result under strictly positive retention, and additive and multiplicative decompositions for sequential design and detector channels. We also separate response dependence from disturbance of shared marginals and clarify why outcomes of unchosen incompatible contexts are not model-neutral missing entries. The theory is evaluated on the perfect-anticorrelation three-cycle, the Klyachko–Can–Binicioğlu–Shumovsky pentagon, and the Peres–Mermin magic square. The hidden-variable and inequality-constrained optimizations agree to within 10 − 12 nats. Exhaustive enumeration of all 104 context subcovers shows that, for these three canonical benchmark points, every proper subcover is noncontextual. A 51 × 51 scan of a tunable outcome-dependent loss family confirms that exact population hiding occurs only on the zero-retention boundary, while finite-sample detectability can deteriorate well before that boundary. For a known finite-alphabet erasure channel with cellwise retention probabilities we give an exact identification criterion, regular asymptotic and Fieller inference for FMCI, and diagnostics that withhold scalar ratio inference near the noncontextual boundary. Unknown outcome-dependent loss is handled by a calibration-constrained sensitivity workflow and union confidence sets. FMCI is therefore a conditional diagnostic of information attenuation under a declared observation channel, not a replacement for loophole-free contextuality certification.
Source: New Journal of Physics
Authors: Arash Esmaili Zaghi, Ofer Harel, Kun Chen
Institution: University of Connecticut
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,610
OpenAlex ID: W7202355529