Entanglement Negativity in Many-Body Systems: Its Measurement & Applications

We will describe how a genuine measure of mixed state entanglement between two non-complementary parts of a many-body system, namely the negativity, can be measured using a very few replicas of a system (say, in a quantum simulator) and machine learning techniques. We will also illustrate how this can give us insight into the  entanglement structure of many-body states, particularly about the entanglement  accross a many-body localization transition. We will also discuss how another measure stemming from quantum information theory, namely the Holevo information, can be used to capture the memory of many-body localized states.