Efficient Quantum Key Distribution

An important question in quantum communications is how quickly quantum keys can, in principle, be distributed via a communication channel in the presence of noise and loss. While exact results for this quantum capacity have been found in special cases and both upper and lower bounds have been found for certain models, the general exact result for the highest rate at which this information can possibly be securely distributed via a noisy and lossy quantum channel is unknown.

Starting with toy models previous explored in the literature, the project would aim to tighten both the upper and lower bounds for this quantum capacity. This would ultimately be done analytically using tools from quantum Shannon theory. However, we would also guide our analytical research using numerical methods.

Ideally, we would obtain exact results for the quantum capacities of important channels but, failing this, a tightening of the best known bounds would still be a useful result both for theorists and experimentalists.