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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.
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.
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
Includes supplementary material: [...]
Mathematical symbols.- 1 Introduction.- 2 Partial orders and Pontryagin duality.- 3 The ring ¿ (d).- 4 Quantum systems with variables in ¿ (d).- 5 Finite Geometries and Mutually Unbiased Bases.- 6 Quantum logic of finite quantum systems.- 7 Galois fields.- 8 Quantum systems with variables in GF(pe).- 9 p-adic numbers and profinite groups.- 10 A quantum system with positions in the profinite group ¿p.- 11 A quantum system with positions in the profinite group ¿.- Index.
| Erscheinungsjahr: | 2017 |
|---|---|
| Fachbereich: | Theoretische Physik |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Physik, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xiii
196 S. 3 s/w Illustr. 4 farbige Illustr. 196 p. 7 illus. 4 illus. in color. |
| ISBN-13: | 9783319594941 |
| ISBN-10: | 331959494X |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-59494-1 |
| Einband: | Gebunden |
| Autor: | Vourdas, Apostolos |
| Auflage: | 1st edition 2017 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 17 mm |
| Von/Mit: | Apostolos Vourdas |
| Erscheinungsdatum: | 28.07.2017 |
| Gewicht: | 0,527 kg |
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
Includes supplementary material: [...]
Mathematical symbols.- 1 Introduction.- 2 Partial orders and Pontryagin duality.- 3 The ring ¿ (d).- 4 Quantum systems with variables in ¿ (d).- 5 Finite Geometries and Mutually Unbiased Bases.- 6 Quantum logic of finite quantum systems.- 7 Galois fields.- 8 Quantum systems with variables in GF(pe).- 9 p-adic numbers and profinite groups.- 10 A quantum system with positions in the profinite group ¿p.- 11 A quantum system with positions in the profinite group ¿.- Index.
| Erscheinungsjahr: | 2017 |
|---|---|
| Fachbereich: | Theoretische Physik |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Physik, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xiii
196 S. 3 s/w Illustr. 4 farbige Illustr. 196 p. 7 illus. 4 illus. in color. |
| ISBN-13: | 9783319594941 |
| ISBN-10: | 331959494X |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-59494-1 |
| Einband: | Gebunden |
| Autor: | Vourdas, Apostolos |
| Auflage: | 1st edition 2017 |
| Hersteller: | Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 17 mm |
| Von/Mit: | Apostolos Vourdas |
| Erscheinungsdatum: | 28.07.2017 |
| Gewicht: | 0,527 kg |
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