2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90913We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to bring these to the attention of the statistical community.19 pages, submitted to J. Royal Stat. Soc. B. Note added 31/05/04: a revised version with further statistical results but less mathematical details, and with co-author Luis Artiles, has been posted on arXiv as math.ST/0405595Quantum Physicstext