Some thoughts about the Quantum Van Trees inequality

When a parameter of a quantum system is a random variable, the Quantum Van Trees inequality can be used to check if the combination of quantum measurement and estimator minimizes the error. In this talk we argue that, in general, the Quantum Van Trees inequality can not be saturated; when this happens it is not possible to use it to know if we are using the best measurement strategy. We propose a modification of the Quantum Van Trees inequality and discuss possible applications.