Quantum communication with side infromation

Quantum communication capacities refer to the maximum amount of quantum information that can be reliably transmitted through a noisy communication channel. However, evaluating these capacities for many quantum channels is challenging due to the superadditivity phenomenon. In this thesis, we tackle this problem by proposing the design of multiple degradable extensions for different important discrete and continuous variable channels. By introducing these extensions, we can establish upper bounds on the quantum and private capacities of the original channels. These extended channels often rely on a set of sufficient conditions that determine the degradability of flagged extensions, which are channels formed as convex combinations of other channels with some side information, commonly referred to as flags. Verifying these conditions is straightforward and greatly simplifies the process of constructing degradable extensions. This approach not only provides a practical solution for estimating the capacities of realistic channels but also enhances our understanding of their behavior in terms of degradability. We apply this technique to both discrete and continuous variable channels, expanding its applicability across different scenarios.