000			02081 a2200181 4500
020			_a9783319452395
040			_cIIT Kanpur
041			_aeng
082			_a530.12 _bH323g
100			_aHayashi, Masahito
245			_aA group theoretic approach to quantum information _cMasahito Hayashi
260			_bSpringer _c2017 _aSwitzerland
300			_axiii, 228p
520			_aThis book is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solutions without assuming the asymptotic setting. Next, this book addresses the quantum error correcting code with the symmetric structure of Weyl-Heisenberg groups. This structure leads to understand the quantum error correcting code systematically. Finally, this book focuses on the quantum universal information protocols by using the group SU(d). This topic can be regarded as a quantum version of the Csiszar-Korner's universal coding theory with the type method. The required mathematical knowledge about group representation is summarized in the companion book, Group Representation for Quantum Theory.
650			_aQuantum computers
650			_aGroup theory
942			_cBK _01
999			_c559323 _d559323