Mixed-state entanglement as a diagnostic for quasiparticles and finite-T topological order

Quantum entanglement of pure states has led to new insights into a wide variety of topics. Entanglement of mixed states is however less well understood. In this talk I will focus on a few themes where mixed-state entanglement leads to new insights that are difficult to obtain otherwise. I will mainly focus on two topics: (i) Characterizing finite-temperature topological order (ii) Detecting presence/absence of quasiparticles. Time permitting, I will also discuss a relation between mixed-state entanglement and information obtained from projective measurements, and its application to characterizing multi-component systems, such as quantum disentangled liquids and Kondo lattice systems.