2001/12/17 by Kazuyuki Fujii, Fujii, Kazuyuki
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0112090
Latex file, 72 pages. This is a review article based on my talks given at several universities in Japan and I am preparing this for the forthcoming 10th Numazu Meeting. I made some changes to become more instructive
openalex publication_date 2001/12/17 · arxiv created 2002/01/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate students or non--experts who are interested in both Geometry and Quantum Information Theory. In the first half we make a general review of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1) from the geometric point of view and, in particular, prove that each resolution of unity can be obtained by the curvature form of some bundle on the parameter space. In the latter half we apply a method of generalized coherent states to some important topics in Quantum Information Theory, in particular, swap of coherent states and cloning of coherent ones. We construct the swap operator of coherent states by making use of a generalized coherent operator based on su(2) and show an "imperfect cloning" of coherent states, and moreover present some related problems. In conclusion we state our dream, namely, a construction of \bf Geometric Quantum Information Theory.