General non-additive entropic forms and the inference of quantum density operators

We discuss a general formalism for the inference of quantum density operators from incomplete information, based on the maximization of general non-additive entropic forms, and its application to the reconstruction of mixed states of composite quantum systems from generalized Bell measurements. The method provides a direct way to infer least biased densities with minimum entanglement for any data determined by Bell constraints in two qubit systems, in contrast with the conventional scheme based on the von Neumann entropy. In particular, it is shown that in this case fake entanglement is always avoided for large q when the Tsallis entropy is employed.