This is a second in a series of problem sheets from the UCL course on quantum computing and quantum information. It might be easier to read it on the nbviewer site.
The first problem looks at quantum teleportation in the case where there is uncertainty as to the state of the shared resource. That is to say: quantum teleportation in the when the shared resource is a mixed state. The question asks to determine the average fidelity of the teleportation in such a setup.
The second problem is again about noise, this time in the context of the BB84 quantum key distribution protocol. Alice is sending qubits through a noisy channel to Bob. The question gives you the Kraus operators that define the noise in the channel and asks you to calculate the probability of error in Bob’s read-out due to the noise.