2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213160In the framework of quantum optics, we study the problem of goodness-of-fit testing in a severely ill-posed inverse problem. A novel testing procedure is introduced and its rates of convergence are investigated under various smoothness assumptions. The procedure is derived from a projection-type estimator, where the projection is done in $\mathbb{L}_2$ distance on some suitably chosen pattern functions. The proposed methodology is illustrated with simulated data sets.Published in at http://dx.doi.org/10.1214/08-EJS286 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62G05, 62G10, 62G20 (Primary) 81V80 (Secondary)text