Final Activity Report Summary - ASTQIT (Applications of the Schur Transform to Quantum Information Theory) Quantum computation and communication represent qualitative new methods of information processing, with potentially revolutionary applications to cryptography, algorithms and other tasks. However, many current proposals for quantum communication protocols require impractical amounts of computation on the sending and receiving sides. Our proposal was to use a particular mathematical tool, known as Schur duality, to provide computationally efficient methods for implementing these protocols on quantum computers. During the project we produced a number of efficient new quantum algorithms for use in communication tasks. One of the most significant algorithms was known as the Schur transform. This converted quantum information from a standard form into an alternative form, known as the Schur basis, in which certain manipulations relevant to communication were more readily carried out.