2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/91476The Hughston-Jozsa-Wootters theorem shows that any finite ensemble of quantum states can be prepared "at a distance", and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules. In this paper, we prove a generalized HJW theorem for arbitrary ensembles of states on a C*-algebra. We then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems, and quantum systems with Abelian superselection rules.21 pages, LaTeX. Version 2: Proofs expanded and made more self-contained; added an example of a bit commitment protocol with continuous ensemblesQuantum PhysicsMathematical PhysicsOperator Algebrastext