Quantum uncertainty structures A bayesian approach to quantum randomness
Langue : Anglais
Auteur : PÉREZ-SUÁREZ Marcos
Quantum Uncertainty Structures - A Bayesian Approach to Quantum
Randomness, is the first full-sized monograph on the implications of
Bayesian probability theory in regards to the structural elements and
procedures of quantum information. The irreducibility and algebraic
features of quantum randomness are introduced through a discussion of
Bell-type inequalities and the Kochen-Specker theorem in terms of the
interplay of quantum states, PVMs, POVMs, and Kraus rule. The, the meaning
of the analysis of randomness is considered in terms of probability theory
from stated first principles, concluding that it refers to the coherent
and adaptive arrangement of personal uncertainty. Finally, the elements
comprising the structural framework of quantum information, namely,
quantum states and operations, are shown to be uncertainty encoding
structures much in the same way as probability assignments, albeit with
intriguing differences explored throughout the book. Algebraic structures
such as entangled quantum states and SIC-POVMs, which are well known in
the applications of quantum information processing, are proven to be
instrumental in this setting, thus strengthening their relevance.
Significant features of the book include:
- first and comprehensive monograph on a Bayesian approach to quantum
information
- clear and thorough discussion of foundations and implications
- detailed description of algebraic procedures and analytical results
- a novel analysis of Kraus rule as a conditioning procedure
- further emphasis on the significance of SIC-POVMs in regards to quantum
information.
This book will be of interest to a wide audience, ranging from graduate-level
students in physics, mathematics and philosophy, to senior researchers in
the fields of quantum theory and quantum information, linear algebra,
operator theory on Hilbert space, probability theory, philosophy, or the
history of physics.
The book is self-contained, with only a basic working knowledge of the
elements of quantum information being assumed on the part of the reader.
It could be used as a textbook for selected topics in advanced
undergraduate courses on quantum theory and quantum information.
A skeleton key to the structural elements.- Systems and quantum systems.-
Quantum states.- Composite quantum systems.- Quantum analysis of data
generation.- Closed quantum systems.- Unitary processing.- Open quantum
systems.- Generalized processing.- First implications.- On the
irreducibility of quantum randomness.- Classical structures of
uncertainty.- Objective probability.- Non-objective probability.- Quantum
structures of uncertainty.- Quantum states.- Quantum conditioning.-
Quantum operations.- Quantum 'tomography' and the Quantum de Finetti
representations.- Compatibility of quantum states assignments.-
Conclusions and further research.- Bruno de Finetti's Probabilism.- The
Kolmogorov Axiom System.
Date de parution : 07-2013
Ouvrage de 200 p.
15.5x23.5 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 104,81 €
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