This volume, setting out the theory of positive maps as it
stands today, reflects the rapid growth in this area of mathematics
since it was recognized in the 1990s that these applications of
C*-algebras are crucial to the study of entanglement in quantum
theory. The author, a leading authority on the subject, sets out
numerous results previously unpublished in book form. In addition
to outlining the properties and structures of positive linear maps
of operator algebras into the bounded operators on a Hilbert space,
he guides readers through proofs of the Stinespring theorem and its
applications to inequalities for positive maps.
The text examines the maps positivity properties, as well as
their associated linear functionals together with their density
operators. It features special sections on extremal positive maps
and Choi matrices. In sum, this is a vital publication that covers
a full spectrum of matters relating to positive linear maps, of
which a large proportion is relevant and applicable to today s
quantum information theory. The latter sections of the book present
the material in finite dimensions, while the text as a whole
appeals to a wider and more general readership by keeping the
mathematics as elementary as possible throughout."
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