An introduction to non-local quantum computation

In the setting of non-local quantum computation (NLQC), we study how multiple parties can implement channels on a distributed input system by making use of an entangled resource state, local operations, and a single round of communication.
Non-local quantum computation was primarily studied as a means to understand the security of quantum position verification schemes, but it is also related to information theoretic cryptography and the AdS/CFT correspondence.
I will first give a basic introduction to the setting, known connections to other fields and important results about NLQC. Afterwards, i will talk about how we can study the relative hardness of different NLQC tasks by showing reductions between them.