03623nmm a2200409 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002300139245024700162250001700409260005600426300003100482505015000513653002000663653002400683653002200707653002400729653002200753653002500775653002000800653002500820653003600845700003100881700002700912041001900939989003600958490002900994028003001023856007201053082001101125520052201136520097601658520057902634EB001033913EBX0100000000000000082743500000000000000.0cr|||||||||||||||||||||150601 ||| eng a97833191671831 aGupta, Ved Prakash00aThe Functional Analysis of Quantum Information TheoryhElektronische RessourcebA Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Wintercby Ved Prakash Gupta, Prabha Mandayam, V.S. Sunder a1st ed. 2015 aChambSpringer International Publishingc2015, 2015 aXI, 139 pbonline resource0 aPreface -- Operator Spaces -- Entanglement in Bipartite Quantum States -- Operator Systems -- Quantum Information Theory -- Index -- Bibliography aQuantum Physics aFunctional analysis aQuantum computers aFunctional Analysis aQuantum Computing aMathematical Physics aQuantum physics aMathematical physics aMathematical Methods in Physics1 aMandayam, Prabhae[author]1 aSunder, V.S.e[author]07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes in Physics50a10.1007/978-3-319-16718-340uhttps://doi.org/10.1007/978-3-319-16718-3?nosfx=yxVerlag3Volltext0 a530.12 aStarting from the basic definitions of operator spaces and operator systems, this text proceeds to discuss several important theorems including Stinespring’s dilation theorem for completely positive maps and Kirchberg’s theorem on tensor products of C*-algebras. It also takes a closer look at the abstract characterization of operator systems and, motivated by the requirements of different tensor products in quantum information theory, the theory of tensor products in operator systems is discussed in detail. aThis book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers of operator algebras, which forms the underpinning of most current mathematical treatments of the quantum theory, besides being one of the most dynamic areas of twentieth century functional analysis. Today, von Neumann’s foresight finds expression in the rapidly growing field of quantum information theory. These notes gather the content of lectures given by a very distinguished group of mathematicians and quantum information theorists, held at the IMSc in Chennai some years ago, and great care has been taken to present the material as a primer on the subject matter. aOn the quantum information side, the book offers a rigorous treatment of quantifying entanglement in bipartite quantum systems, and moves on to review four different areas in which ideas from the theory of operator systems and operator algebras play a natural role: the issue of zero-error communication over quantum channels, the strong subadditivity property of quantum entropy, the different norms on quantum states and the corresponding induced norms on quantum channels, and, lastly, the applications of matrix-valued random variables in the quantum information setting