Finite and Profinite Quantum Systems

  • Apostolos┬áVourdas

Part of the Quantum Science and Technology book series (QST)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Apostolos Vourdas
    Pages 1-6
  3. Apostolos Vourdas
    Pages 7-10
  4. Apostolos Vourdas
    Pages 11-21
  5. Apostolos Vourdas
    Pages 57-76
  6. Apostolos Vourdas
    Pages 77-91
  7. Apostolos Vourdas
    Pages 93-105
  8. Apostolos Vourdas
    Pages 107-117
  9. Apostolos Vourdas
    Pages 119-143
  10. Apostolos Vourdas
    Pages 145-160
  11. Back Matter
    Pages 195-196

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.


Finite quantum systems Galois fields Profinite groups Mutually unbiased bases Quantum Logic Heisenberg-Weyl group Symplectic group

Authors and affiliations

  • Apostolos┬áVourdas
    • 1
  1. 1.Department of Computer ScienceUniversity of BradfordBradfordUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-59494-1
  • Online ISBN 978-3-319-59495-8
  • Series Print ISSN 2364-9054
  • Series Online ISSN 2364-9062
  • Buy this book on publisher's site