1.

Record Nr.

UNISA996466521003316

Autore

Aubrun Guillaume

Titolo

Quantum Symmetries [[electronic resource] ] : Metabief, France 2014 / / by Guillaume Aubrun, Adam Skalski, Roland Speicher ; edited by Uwe Franz

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

ISBN

3-319-63206-X

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (IX, 119 p. 18 illus., 3 illus. in color.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2189

Disciplina

515.7

Soggetti

Functional analysis

Quantum physics

Probabilities

Convex geometry 

Discrete geometry

Functional Analysis

Quantum Physics

Probability Theory and Stochastic Processes

Convex and Discrete Geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

1 Introduction -- 2 Free Probability and Non-Commutative Symmetries -- 3 Quantum Symmetry Groups and Related Topics -- 4 Quantum Entanglement in High Dimensions -- References -- Index.

Sommario/riassunto

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.  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.