Escort Density Operators and Generalized Quantum Information Measures

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 ϕ-exponential family is introduced. This family, together with its escort, optimizes the generalized lower bound. It also satisfies a maximum entropy principle and exhibits a thermodynamic structure in which entropy and free energy are related by Legendre transform.