Over the last 15 years a fruitful collaboration between techniques and concepts from Quantum Information and Condensed Matter Physics gave rise to ideas such as Density Matrix Renormalization Group (DMRG), Topological Entanglement Entropy, Projected Entangled Pair States (PEPs) and MERA. My talk will focus on one particular area of interplay between Condensed Matter and Quantum Information, which has been called
to Quantum Phase Transitions (QPTs). Distinguishing between two quantum states is at the core of many quantum information processing tasks. The fidelity quantifies such degree of distinguishability and it provides a useful information-theoretic framework that encompasses all critical phenomena.
In this talk I will focus on its applicability to study QPTs involving topological phases, and describe its advantages and limitations. Time permitting I will also mention my joint work with Masoud Mohseni and Seth Lloyd on Quantum Biology.