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The Functional Analysis of Quantum Information Theory - A Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter (Paperback, 2015 ed.)
Loot Price: R1,733
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The Functional Analysis of Quantum Information Theory - A Collection of Notes Based on Lectures by Gilles Pisier, K. R. Parthasarathy, Vern Paulsen and Andreas Winter (Paperback, 2015 ed.)
Series: Lecture Notes in Physics, 902
Expected to ship within 10 - 15 working days
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This 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. Starting
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. On 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.
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