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Parameterized families of density operators are studied. A generalization of the lower bound of Cramér and Rao is formulated. It involves escort density operators. The notion of ø-exponential family is introduced. This family, together with its escort, optimizes the generalized lower bound. It also satis.es a maximum entropy principle and exhibits a thermodynamic structure in which entropy and free energy are related by Legendre transform.

Escort Density Operators and Generalized Quantum Information Measures