A Group Theoretic Approach to Quantum Information

Více o knize

This book uniquely addresses quantum information through the lens of group symmetry, a perspective not covered by existing textbooks despite the abundance of resources on group representation. It begins with the mathematical foundations of quantum information and explores quantum entanglement, utilizing group symmetry to simplify the calculation of various entanglement measures that are typically complex. The text delves into optimal information processes, such as quantum state estimation, cloning, group action estimation, and quantum channels, demonstrating how group symmetry facilitates the derivation of optimal solutions without relying on asymptotic settings. Additionally, the book examines quantum error-correcting codes through the symmetric structure of Weyl-Heisenberg groups, providing a systematic understanding of these codes. It culminates in a discussion of quantum universal information protocols using the group SU(d), which can be seen as a quantum adaptation of Csiszar-Korner's universal coding theory employing the type method. For readers seeking the necessary mathematical background, a companion book summarizes the relevant concepts of group representation for quantum theory.