Suppose we are presented with a language like L = {x ∈ {0, 1}| The third to last bit is 1}. We can intuitively understand this language. Given a string we can quickly tell if it is in L or not.

One of the most active research directions in quantum computing currently is establishing quantum supremacy results: coming up with computational tasks which a quantum algorithm can solve super-polynomially faster than a classical algorithm.

In this thesis we tackle two main problems :
1. Coding techniques for sending quantum information across a multi-terminal quantum channel in the one-shot regime.

Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolutional, Turbo, LDPC and Polar codes: each is a linear code and represents a mathematical breakthrough.