By Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder

This booklet offers readers with a concise advent to present reviews on operator-algebras and their generalizations, operator areas and operator platforms, with a distinct specialize in their software in quantum info technology. This uncomplicated framework for the mathematical formula of quantum details will be traced again to the mathematical paintings of John von Neumann, one of many pioneers of operator algebras, which kinds the underpinning of most present mathematical remedies of the quantum thought, along with being the most dynamic components of 20th century practical research. this present day, von Neumann’s foresight reveals expression within the speedily becoming box of quantum info conception. those notes assemble the content material of lectures given through a truly unusual workforce of mathematicians and quantum details theorists, held on the IMSc in Chennai a few years in the past, and nice care has been taken to offer the fabric as a primer at the material. ranging from the fundamental definitions of operator areas and operator platforms, this article proceeds to debate numerous vital theorems together with Stinespring’s dilation theorem for thoroughly optimistic maps and Kirchberg’s theorem on tensor items of C*-algebras. It additionally takes a more in-depth examine the summary characterization of operator platforms and, stimulated through the necessities of alternative tensor items in quantum details idea, the idea of tensor items in operator platforms is mentioned intimately. at the quantum details aspect, the ebook deals a rigorous therapy of quantifying entanglement in bipartite quantum structures, and strikes directly to overview 4 diverse components within which rules from the idea of operator platforms and operator algebras play a ordinary function: the difficulty of zero-error conversation over quantum channels, the powerful subadditivity estate of quantum entropy, the various norms on quantum states and the corresponding precipitated norms on quantum channels, and, finally, the purposes of matrix-valued random variables within the quantum info environment