Quantum channel simulation and discrimination with applications to quantum communications

Quantum channel discrimination is a highly versatile task in quantum information. Almost any physical process can be modelled as a quantum channel, so discrimination between channels has broad applications across many fields of science. Since the processes modelled by quantum channels and the contexts in which we want to discriminate between them are so wide-ranging, it should come as no surprise that the possible protocols are equally varied. The most general discrimination protocols can use any sequence of operations allowed by physics. This is what makes protocol stretching such a powerful mathematical tool. It allows the calculation of bounds on the performance of any discrimination protocol and can be applied to any situation in which the channels involved are jointly simulable by some quantum processor. Certain channels, such as the amplitude damping channels, cannot be simulated using standard teleportation. Others, like the lossy bosonic channels, can be (individually) simulated using teleportation, but two lossy channels with different losses cannot be jointly simulated. In this thesis, we characterise port-based teleportation so that it can be used as a tool for channel simulation. Port-based teleportation is a variant of quantum teleportation that can simulate any channel in the asymptotic limit of infinite ports. For a finite number of ports, we can find resource states that simulate amplitude damping channels well. By combining our channel simulations with the technique of protocol stretching, we are able to tighten existing bounds on the discrimination of amplitude-damping channels. We also address the relatively unstudied subfield of channel position finding. We use channel simulation to bound the performance of environment localisation, and we show the viability of idler-free channel position finding over pure loss channels. Finally, we calculate the secret key rate for a scenario of quantum hacking based on a side channel in the sender's device.