Decoupling Theorems

Abstract

Decoupling theorems have proven useful in various applications in the area of quantum information theory. This thesis builds upon preceding work by Fr\'{e}d\'{e}ric Dupuis [arXiv:1012.6044v1], where a general decoupling theorem is obtained and its implications for quantum coding theory are studied. At first we generalize this theorem to the case where the average is taken over an approximate unitary 2-design. The second part of this project tackles the question whether or not it is possible to decorrelate CQ-states with classical operations. We obtain results similar to the pivotal Leftover Hash Lemma. Finally we analyze the decoupling power of permutation operators in a fully quantum context and show a general procedure that yields decoupling theorems with permutations.