Introduction to the theory of quantum information processing:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2013
|
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Klappentext Inhaltsverzeichnis |
| Beschreibung: | XI, 150 S. graph. Darst. |
| ISBN: | 9781461470915 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to the theory of quantum information processing |c János A. Bergou ; Mark Hillery |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2013 | |
| 300 | |a XI, 150 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Graduate texts in physics | |
| 650 | 0 | 7 | |a Quanteninformatik |0 (DE-588)4705961-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quanteninformatik |0 (DE-588)4705961-8 |D s |
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| 700 | 1 | |a Hillery, Mark Stephen |d 1951- |e Verfasser |0 (DE-588)103711874X |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4614-7092-2 |
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026103135&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026103135 | ||
Datensatz im Suchindex
| _version_ | 1804150518859169792 |
|---|---|
| adam_text | Contents
1
Introduction
.................................................................. 1
1.1
The Qubit
................................................................ 1
1.2
Quantum Gates
.......................................................... 3
1.3
Quantum Circuits
....................................................... 4
1.4
The
Deutsch
Algorithm
................................................. 5
1.5
Problems
................................................................. 7
References
..................................................................... 8
2
The Density Matrix
.......................................................... 9
2.1
Ensembles and Subsystems
............................................. 9
2.2
Properties
................................................................ 11
2.3
Pure States and Mixed States of a Qubit
............................... 12
2.4
Pure State Decompositions and the Ensemble Interpretation
......... 14
2.5
A Mathematical Aside: The Schmidt Decomposition
of a Bipartite State
...................................................... 17
2.6
Purification, Reduced Density Matrices, and the Subsystem
Interpretation
............................................................ 19
2.7
Problems
................................................................. 19
References
..................................................................... 21
3
Entanglement
................................................................. 23
3.1
Definition of Entanglement
............................................. 23
3.2
Bell Inequalities
......................................................... 24
3.3
Representative Applications of Entanglement:
Dense Coding and
Teleportation
....................................... 27
3.3.1
Dense Coding
................................................... 27
3.3.2
Teleportation
.................................................... 27
3.4
Conditions of Separability
.............................................. 28
3.5
Entanglement Distillation and Formation
.............................. 33
3.5.1
Local Operations and Classical Communication [LOCC]
.... 33
3.5.2
Entanglement Distillation: Procrustean Method
.............. 34
3.5.3
Entanglement Formation
....................................... 34
IX
x
Contents
3
.6
Entanglement Measures
................................................ 35
3.6.1
The
von
Neumann Entropy as an Entanglement
Measure for Pure Bipartite States: A First Set of Properties.
. 35
3.6.2
A Useful Auxiliary Quantity: Relative Entropy
and Klein s Inequality
.......................................... 36
3.6.3
The
von
Neumann Entropy: A Second Set of Properties
..... 37
3.6.4
The Effect of Local Measurements on Entanglement
......... 39
3.6.5
Towards the Entanglement of Mixed States
................... 40
3.6.6
The Effect of Throwing Away Part of the System
Locally on Entanglement
....................................... 40
3.6.7
Bound Entanglement
........................................... 41
3.7
Concurrence
............................................................. 42
3.8
Problems
................................................................. 44
References
..................................................................... 47
4
Generalized Quantum Dynamics
........................................... 49
4.1
Quantum Maps or
Superoperators
...................................... 49
4.1.1
Quantum Maps and Their
Kraus
Representation
.............. 49
4.1.2
Properties of Quantum Maps
................................... 50
4.1.3
Properties of the
Kraus
Operators
.............................. 53
4.2
An Example: The Depolarizing Channel
.............................. 54
4.3
Impossible Maps
........................................................ 55
4.3.1
The Cloning Map and the No-Cloning Theorem
.............. 55
4.3.2
Faster than Light Communication
............................. 56
4.4
Problems
................................................................. 56
References
..................................................................... 58
5
Quantum Measurement Theory
............................................ 59
5.1
Outline
................................................................... 59
5.2
Standard Quantum Measurements
..................................... 59
5.3
Positive Operator Valued Measures
.................................... 63
5.4
Neumark s Theorem and the Implementation of a POVM
Via Generalized Measurements
........................................ 66
5.5
Examples: Strategies for State Discrimination
........................ 70
5.5.1
Unambiguous Discrimination of Two Pure States
............ 71
5.5.2
Minimum-Error Discrimination of Two Quantum States
..... 75
5.6
Problems
................................................................. 79
References
..................................................................... 81
6
Quantum Cryptography
.................................................... 83
6.1
Outline
................................................................... 83
6.2
The One-Time Pad
...................................................... 84
6.3
The B92 Quantum Key Distribution Protocol
......................... 85
6.4
The BB
84
Protocol
..................................................... 86
6.5
The E91 Protocol
........................................................ 88
6.6
Quantum Secret Sharing
................................................ 89
Contents xi
6.7 Problems................................................................. 90
References.....................................................................
91
7 Quantum
Algorithms........................................................
93
7.1 The Deutsch-Jozsa
Algorithm
......................................... 93
7.2
The Bernstein-Vazirani Algorithm
..................................... 95
7.3
Quantum Search: The
Grover
Algorithm
.............................. 96
7.4
Period Finding: Simon s Algorithm
.................................... 101
7.5
Quantum Fourier Transform and Phase Estimation
................... 102
7.6
Quantum Walks
......................................................... 105
7.7
Problems
................................................................. 115
References
..................................................................... 115
8
Quantum Machines
.......................................................... 117
8.1
Introduction
............................................................. 117
8.2
Cloners and U-NOT Gates
.............................................. 117
8.3
Programmable Machines: A General Result
........................... 120
8.4
Probabilistic Processors
................................................. 123
8.5
A Programmable State Discriminator
.................................. 125
8.6
Problems
................................................................. 129
References
..................................................................... 130
9
Decoherence and Quantum Error Correction
............................ 133
9.1
General Theory of Quantum Error-Correcting Codes
................. 133
9.2
An Example: CSS Codes
............................................... 141
9.3
Decoherence-Free Subspaces
........................................... 146
9.4
Problems
................................................................. 148
References
..................................................................... 148
Index
............................................................................... 149
Graduate Texts in Physics
János
A. Bergou
·
Mark Hillery
Introduction to the Theory of Quantum Information Processing
Introduction to the Theory of Quantum Information Processing provides the material
for a one-semester graduate level course on quantum information theory and quantum
computing for students who have had a one-year graduate course in quantum
mechanics. Many standard subjects are treated, such as density matrices, entanglement,
quantum maps, quantum cryptography, and quantum codes. Also included are
discussion*- of quantum machines and quantum walks. In addition, the book provides
detailed treatments of several underlying fundamental principles of quantum theory,
such as quantum measurements, the no-cloning and no-signaling theorems, and their
consequences. Problems of various levels of difficulty supplement the text, with the most
challenging problems bringing the reader to the forefront of active research.
This book provides a compact introduction to the fascinating and rapidly evolving
interdisciplinary field of quantum information theory, and it prepares the reader tor
doing active research in this area.
|
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| isbn | 9781461470915 |
| language | English |
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| spelling | Bergou, János A. 1947- Verfasser (DE-588)1037118685 aut Introduction to the theory of quantum information processing János A. Bergou ; Mark Hillery New York [u.a.] Springer 2013 XI, 150 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 s DE-604 Hillery, Mark Stephen 1951- Verfasser (DE-588)103711874X aut Erscheint auch als Online-Ausgabe 978-1-4614-7092-2 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026103135&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026103135&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bergou, János A. 1947- Hillery, Mark Stephen 1951- Introduction to the theory of quantum information processing Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4705961-8 |
| title | Introduction to the theory of quantum information processing |
| title_auth | Introduction to the theory of quantum information processing |
| title_exact_search | Introduction to the theory of quantum information processing |
| title_full | Introduction to the theory of quantum information processing János A. Bergou ; Mark Hillery |
| title_fullStr | Introduction to the theory of quantum information processing János A. Bergou ; Mark Hillery |
| title_full_unstemmed | Introduction to the theory of quantum information processing János A. Bergou ; Mark Hillery |
| title_short | Introduction to the theory of quantum information processing |
| title_sort | introduction to the theory of quantum information processing |
| topic | Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Quanteninformatik |
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