Entanglement Properties and Quantum Phase Transitions in Interacting Disordered One Dimensional Systems
Interacting disordered one-dimensional fermionic systems are an ideal test ground in order to investigate the interplay between properties of the entanglement and quantum phase transitions. Although 1D systems with uncorrelated disorder are always localized, they may exhibit a quantum phase transition to a metallic phase as function of disorder strength if the disorder is correlated (e.g., the Harper model). Once attractive interactions are considered, a transition to a metallic/superconducting phase is predicted.
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.