Quantum Science and Technology

Finite and Profinite Quantum Systems

Authors: Vourdas, Apostolos

  • Provides a unique overview of finite quantum systems in a pedagogical form suitable for advanced students and researchers alike, presenting theory complemented with examples
  • Offers an introduction to the field at a time of current interest and emerging applications in quantum information and related areas
  • Takes an interdisciplinary approach combining advanced topics in mathematics and condensed matter and quantum physics
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eBook £50.99
price for United Kingdom (gross)
  • ISBN 978-3-319-59495-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £63.99
price for United Kingdom (gross)
  • ISBN 978-3-319-59494-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics.

The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. 

The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers.

Applications of the formalism include quantum optics and quantum computing, two-dimensional electron systems in magnetic fields and the magnetic translation group, the quantum Hall effect, other areas in condensed matter physics, and Fast Fourier Transforms.

The monograph combines ideas from quantum mechanics with discrete mathematics, algebra, and number theory. It is suitable for graduate students and researchers in quantum physics, mathematics and computer science.

About the authors

Apostolos Vourdas is a Professor of Computing at the University of Bradford, UK, with research interests spanning various aspects of quantum computing (analytic functions in quantum physics; algebraic and group theory methods; finite quantum systems; Galois fields and p-adic numbers in quantum computing; quantum logic and lattice theory).  He has published over 160 refereed journal papers and 8 invited review articles, and has an h-index of 34.

Table of contents (12 chapters)

  • Introduction

    Vourdas, Apostolos

    Pages 1-6

  • Partial Orders and Pontryagin Duality

    Vourdas, Apostolos

    Pages 7-10

  • The Ring $${\mathbb Z}(d)$$

    Vourdas, Apostolos

    Pages 11-21

  • Quantum Systems with Variables in $${\mathbb Z}(d)$$

    Vourdas, Apostolos

    Pages 23-55

  • Finite Geometries and Mutually Unbiased Bases

    Vourdas, Apostolos

    Pages 57-76

Buy this book

eBook £50.99
price for United Kingdom (gross)
  • ISBN 978-3-319-59495-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £63.99
price for United Kingdom (gross)
  • ISBN 978-3-319-59494-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Finite and Profinite Quantum Systems
Authors
Series Title
Quantum Science and Technology
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-59495-8
DOI
10.1007/978-3-319-59495-8
Hardcover ISBN
978-3-319-59494-1
Series ISSN
2364-9054
Edition Number
1
Number of Pages
XIII, 196
Number of Illustrations and Tables
3 b/w illustrations, 4 illustrations in colour
Topics