MSc Math Defence: Degradable and Antidegradable Qubit Channels

Connor Paul-Paddock, M.Sc. Thesis Defence

This thesis investigates a characterization for the set of antidegradable qubit channels. The characterization comes from a correspondence between the antidegradability of a channel, and the symmetric extendibility of the Choi operator.  Using an inequality intended to describe the set of bipartite qubit states which admit symmetric extension, we demonstrate that it additionally provides a condition to characterize the set of antidegradable qubit channels. Using the characterization we investigate the antidegradability of qubit channels with respect to the rank of the Choi matrix. We also apply the antidegradability criterion to the qubit amplitude damping and qubit depolarizing channel. We end by discussing degradable and antidegradable channels in terms of their channel capacities and the applications of these results to investigating phenomena such as super-additive coherent information and superactivation.

A copy of the thesis is available (pdf format) from Susan McCormick for examination and comment.