Information-Theoretical Criteria for Characterizing the Earliness of Time-Series Data.

Biomedical signals constitute time-series that sustain machine learning techniques to achieve classification. These signals are complex with measurements of several features over, eventually, an extended period. Characterizing whether the data can anticipate prediction is an essential task in time-series mining.

Information geometric analysis of long range topological superconductors.

The Uhlmann connection is a mixed state generalisation of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretical quantity which is a measure of distinguishability of quantum states.

Uhlmann Connection in Fermionic Systems Undergoing Phase Transitions.

We study the behavior of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyze some of the paradigmatic cases of topological insulators and superconductors in one dimension, as well as the BCS theory of superconductivity in three dimensions. We show that the Uhlmann connection signals phase transitions in which the eigenbasis of the state of the system changes.

Macroscopic distinguishability between quantum states defining different phases of matter: fidelity and the Uhlmann geometric phase.

We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: The Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition.

Ground state overlap and quantum phase transitions.

We present a characterization of quantum phase transitions in terms of the the overlap function between two ground states obtained for two different values of external parameters. On the examples of the Dicke and XY models, we show that the regions of criticality of a system are marked by the extremal points of the overlap and functions closely related to it. Further, we discuss the connections between this approach and the Anderson orthogonality catastrophe as well as with the dynamical study of the Loschmidt echo for critical systems.