Quantum Symmetries: Metabief, France 2014 (lecture Notes In Mathematics)
by Roland Speicher /
2017 / English / PDF
4.4 MB Download
Providing an introduction to current research topics in
functional analysis and its applications to quantum physics, this
book presents three lectures surveying recent progress and open
problems.
Providing an introduction to current research topics in
functional analysis and its applications to quantum physics, this
book presents three lectures surveying recent progress and open
problems.
A special focus is given to the role of symmetry in
non-commutative probability, in the theory of quantum groups, and
in quantum physics. The first lecture presents the close
connection between distributional symmetries and independence
properties. The second introduces many structures (graphs,
C*-algebras, discrete groups) whose quantum symmetries are much
richer than their classical symmetry groups, and describes the
associated quantum symmetry groups. The last lecture shows how
functional analytic and geometric ideas can be used to detect and
to quantify entanglement in high dimensions.
A special focus is given to the role of symmetry in
non-commutative probability, in the theory of quantum groups, and
in quantum physics. The first lecture presents the close
connection between distributional symmetries and independence
properties. The second introduces many structures (graphs,
C*-algebras, discrete groups) whose quantum symmetries are much
richer than their classical symmetry groups, and describes the
associated quantum symmetry groups. The last lecture shows how
functional analytic and geometric ideas can be used to detect and
to quantify entanglement in high dimensions.
The book will allow graduate students and young researchers to
gain a better understanding of free probability, the theory of
compact quantum groups, and applications of the theory of Banach
spaces to quantum information. The latter applications will also
be of interest to theoretical and mathematical physicists working
in quantum theory.
The book will allow graduate students and young researchers to
gain a better understanding of free probability, the theory of
compact quantum groups, and applications of the theory of Banach
spaces to quantum information. The latter applications will also
be of interest to theoretical and mathematical physicists working
in quantum theory.
