  We examine the inference of quantum density operators from incomplete
information by means of the maximization of general non-additive entropic
forms. Extended thermodynamic relations are given. When applied to a bipartite
spin 1/2 system, the formalism allows to avoid fake entanglement for data based
on the Bell-CHSH observable, and, in general, on any set of Bell constraints.
Particular results obtained with the Tsallis entropy and with an introduced
exponential entropic form are also discussed.
