This module we get our hands dirty by tackling the fundamental difficulties of working with many-qubit states in quantum information. As we will soon see the question “what is the state of a quantum system” is not an easy one to answer in general.

We are going to have to extend significantly the formalism for representing qubits that we saw in week zero in order to be able to describe arbitrary quantum systems, including one of many qubits. This will be extremely important in cryptography, where we need a way to talk about the joint state of multiple users (and the adversary), as well as have ways to describe just a single user, or two honest users, without needing to refer to an unknown adversary.