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This book presents readers with a concise introduction to current analysis on operator-algebras and their generalizations, operator areas and operator methods, with a specific focus on their software in quantum information science. This main framework for the mathematical formulation of quantum information is perhaps traced once more to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which varieties the underpinning of most current mathematical cures of the quantum idea, in addition to being one of in all probability probably the most dynamic areas of twentieth century sensible analysis. In the mean time, von Neumann’s foresight finds expression in the shortly rising topic of quantum information precept. These notes acquire the content material materials of lectures given by a very distinguished group of mathematicians and quantum information theorists, held on the IMSc in Chennai some years in the previous, and good care has been taken to present the material as a primer on the topic materials. Starting from the important definitions of operator areas and operator strategies, this textual content material proceeds to debate a quantity of important theorems along with Stinespring’s dilation theorem for completely constructive maps and Kirchberg’s theorem on tensor merchandise of C*-algebras. It moreover takes a greater check out the abstract characterization of operator methods and, motivated by the requirements of completely totally different tensor merchandise in quantum information precept, the thought of tensor merchandise in operator methods is talked about in factor. On the quantum information facet, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum strategies, and strikes on to analysis four completely totally different areas in which ideas from the thought of operator methods and operator algebras play a pure place: the problem of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the completely totally different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the needs of matrix-valued random variables in the quantum information setting.
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