The Description of Joint Quantum Entities and the Formulation of a Paradox

We formulate a paradox in relation to the description of a joint entity consisting of two subentities by standard quantum mechanics. We put forward a proposal for a possible solution, entailing the interpretation of density states as pure states. We explain where the inspiration for this proposal comes from and how its validity can be tested experimentally. We discuss the consequences on quantum axiomatics of the proposal.