We examine the inference of quantum density operators from incomplete information by means of the maximization of general nonadditive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system, the formalism allows one to avoid fake entanglement for data based on the Bell-Clauser-Horne-Shimony-Holt 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.Facultad de Ciencias Exactas