Introduction to quantum information science:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2006
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford graduate texts
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Beschreibung für Leser Inhaltsverzeichnis |
| Beschreibung: | X, 183 S. Ill., graph. Darst. |
| ISBN: | 9780199215706 0199215707 9780199673483 |
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| 100 | 1 | |a Vedral, Vlatko |e Verfasser |0 (DE-588)141133368 |4 aut | |
| 245 | 1 | 0 | |a Introduction to quantum information science |c Vlatko Vedral |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2006 | |
| 300 | |a X, 183 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804136182483779585 |
|---|---|
| adam_text | Contents
PART I CLASSICAL AND QUANTUM INFORMATION
1
Classical information
3
1.1
Information and physics
3
1.2
Quantifying information
4
1.3
Data compression
7
1.4
Related measures of information
8
1.4.1
Relative entropy
9
1.4.2
Joint entropy
10
1.4.3
Conditional entropy
10
1.4.4
Mutual information
10
1.5
Capacity of a noisy channel
11
1.6
Summary
12
2
Quantum mechanics
14
2.1
Dirac notation
14
2.2
The qubit, higher dimensions, and the inner product
16
2.3
Hubert spaces
17
2.4
Projective
measurements and operations
19
2.5
Unitary operations
20
2.6
Eigenvectors and eigenvalues
21
2.7
Spectral decomposition
22
2.8
Applications of the spectral theorem
23
2.9
Dirac notation shorthands
24
2.10
The Mach-Zehnder interferometer
25
2.11
The postulates of quantum mechanics
27
2.12
Mixed states
28
2.13
Entanglement
29
2.14
Summary
30
3
Quantum information
—
the basics
31
3.1
No cloning of quantum bits
31
3.2
Quantum cryptography
33
3.3
The trace and partial-trace operations
35
3.4
Hubert space extension
37
3.5
The Schmidt decomposition
38
viii CONTENTS
3.6
Generalized measurements
40
3.7
CP-maps and positive operator-valued measurements
41
3.8
The postulates of quantum mechanics revisited
42
3.9
Summary
42
4
Quantum communication with entanglement
44
4.1
Pure state entanglement and
Pauli
matrices
44
4.2
Dense coding
45
4.3
Teleportation
46
4.4
Entanglement swapping
48
4.5
No instantaneous transfer of information
49
4.6
The extended—Hubert—space view
50
4.7
Summary
50
5
Quantum information I
52
5.1
Fidelity
53
5.2
Helstrom s discrimination
54
5.3
Quantum data compression
55
5.4
Entropy of observation
58
5.5
Conditional entropy and mutual information
59
5.6
Relative entropy
61
5.7
Statistical interpretation of relative entropy
62
5.8
Summary
66
6
Quantum information II
68
6.1
Equalities and inequalities related to entropy
68
6.2
The Holevo bound
71
6.3
Capacity of a bosonic channel
73
6.4
Information gained through measurements
75
6.5
Relative entropy and thermodynamics
76
6.6
Entropy increase due to erasure
77
6.7
Landauer s erasure and data compression
78
6.8
Summary
78
PART II QUANTUM ENTANGLEMENT
7
Quantum entanglement
—
introduction
81
7.1
The historical background of entanglement
81
7.2
Bell s inequalities
83
7.3
Separable states
85
7.4
Pure states and Bell s inequalities
86
7.5
Mixed states and Bell s inequalities
87
7.6
Entanglement in second quantization
87
7.7
Summary
91
8
Witnessing quantum entanglement
92
8.1
Entanglement witnesses
93
8.2
The Jamiolkowski isomorphism
95
CONTENTS ¡x
8.3
The Peres-Horodecki criterion
97
8.4
More examples of entanglement witnesses
99
8.5
Summary
100
9
Quantum entanglement in practice
102
9.1
Measurements with a Mach-Zehnder interferometer
102
9.2
Interferometrie
implementation of Peres-Horodecki criterion
104
9.2.1
Measuring tr
ρ2?
104
9.2.2
Generalization to tr gk
105
9.2.3
Measuring tr (gTa)fc
106
9.3
Measuring the fidelity between
ρ
and
σ
106
9.4
Summary
107
10
Measures of entanglement
108
10.1
Distillation of multiple copies of a pure state
108
10.2
Analogy with the Carnot Cycle
110
10.3
Properties of entanglement measures 111
10.4
Entanglement of pure states
113
10.5
Entanglement of mixed states
113
10.6
Measures of entanglement derived from relative entropy
117
10.7
Classical information and entanglement
121
10.8
Entanglement and thermodynamics
123
10.9
Summary
128
PART III QUANTUM COMPUTATION
11
Quantum algorithms
131
11.1
Computational complexity
131
11.2
Deutsch s algorithm
133
11.2.1
Deutsch s algorithm and the Holevo bound
135
11.3
Oracles
136
11.4
Grover s search algorithm
137
11.5
Quantum factorization
140
11.5.1
Factorization
141
11.5.2
The quantum Fourier transform
142
11.5.3
Phase estimation
144
11.6
Summary
145
12
Entanglement, computation and quantum measurements
146
12.1
Optimization of searches using entanglement
147
12.2
Model for quantum measurement
149
12.3
Correlations and quantum measurement
151
12.4
The ultimate limits of computation: the Bekenstein bound
157
12.5
Summary
158
13
Quantum error correction
160
13.1
Introduction
160
13.2
A simple example
160
χ
CONTENTS
13.3
General conditions
162
13.4
Reliable
quantum
computation
165
13.5
Quantum
error
correction
considered as a Maxwell s demon
167
13.5.1
Pure states
171
13.5.2
Mixed states
172
13.6
Summary
173
14
Outlook
175
Bibliography
179
Index
181
|
| adam_txt |
Contents
PART I CLASSICAL AND QUANTUM INFORMATION
1
Classical information
3
1.1
Information and physics
3
1.2
Quantifying information
4
1.3
Data compression
7
1.4
Related measures of information
8
1.4.1
Relative entropy
9
1.4.2
Joint entropy
10
1.4.3
Conditional entropy
10
1.4.4
Mutual information
10
1.5
Capacity of a noisy channel
11
1.6
Summary
12
2
Quantum mechanics
14
2.1
Dirac notation
14
2.2
The qubit, higher dimensions, and the inner product
16
2.3
Hubert spaces
17
2.4
Projective
measurements and operations
19
2.5
Unitary operations
20
2.6
Eigenvectors and eigenvalues
21
2.7
Spectral decomposition
22
2.8
Applications of the spectral theorem
23
2.9
Dirac notation shorthands
24
2.10
The Mach-Zehnder interferometer
25
2.11
The postulates of quantum mechanics
27
2.12
Mixed states
28
2.13
Entanglement
29
2.14
Summary
30
3
Quantum information
—
the basics
31
3.1
No cloning of quantum bits
31
3.2
Quantum cryptography
33
3.3
The trace and partial-trace operations
35
3.4
Hubert space extension
37
3.5
The Schmidt decomposition
38
viii CONTENTS
3.6
Generalized measurements
40
3.7
CP-maps and positive operator-valued measurements
41
3.8
The postulates of quantum mechanics revisited
42
3.9
Summary
42
4
Quantum communication with entanglement
44
4.1
Pure state entanglement and
Pauli
matrices
44
4.2
Dense coding
45
4.3
Teleportation
46
4.4
Entanglement swapping
48
4.5
No instantaneous transfer of information
49
4.6
The extended—Hubert—space view
50
4.7
Summary
50
5
Quantum information I
52
5.1
Fidelity
53
5.2
Helstrom's discrimination
54
5.3
Quantum data compression
55
5.4
Entropy of observation
58
5.5
Conditional entropy and mutual information
59
5.6
Relative entropy
61
5.7
Statistical interpretation of relative entropy
62
5.8
Summary
66
6
Quantum information II
68
6.1
Equalities and inequalities related to entropy
68
6.2
The Holevo bound
71
6.3
Capacity of a bosonic channel
73
6.4
Information gained through measurements
75
6.5
Relative entropy and thermodynamics
76
6.6
Entropy increase due to erasure
77
6.7
Landauer's erasure and data compression
78
6.8
Summary
78
PART II QUANTUM ENTANGLEMENT
7
Quantum entanglement
—
introduction
81
7.1
The historical background of entanglement
81
7.2
Bell's inequalities
83
7.3
Separable states
85
7.4
Pure states and Bell's inequalities
86
7.5
Mixed states and Bell's inequalities
87
7.6
Entanglement in second quantization
87
7.7
Summary
91
8
Witnessing quantum entanglement
92
8.1
Entanglement witnesses
93
8.2
The Jamiolkowski isomorphism
95
CONTENTS ¡x
8.3
The Peres-Horodecki criterion
97
8.4
More examples of entanglement witnesses
99
8.5
Summary
100
9
Quantum entanglement in practice
102
9.1
Measurements with a Mach-Zehnder interferometer
102
9.2
Interferometrie
implementation of Peres-Horodecki criterion
104
9.2.1
Measuring tr
ρ2?
104
9.2.2
Generalization to tr gk
105
9.2.3
Measuring tr (gTa)fc
106
9.3
Measuring the fidelity between
ρ
and
σ
106
9.4
Summary
107
10
Measures of entanglement
108
10.1
Distillation of multiple copies of a pure state
108
10.2
Analogy with the Carnot Cycle
110
10.3
Properties of entanglement measures 111
10.4
Entanglement of pure states
113
10.5
Entanglement of mixed states
113
10.6
Measures of entanglement derived from relative entropy
117
10.7
Classical information and entanglement
121
10.8
Entanglement and thermodynamics
123
10.9
Summary
128
PART III QUANTUM COMPUTATION
11
Quantum algorithms
131
11.1
Computational complexity
131
11.2
Deutsch's algorithm
133
11.2.1
Deutsch's algorithm and the Holevo bound
135
11.3
Oracles
136
11.4
Grover's search algorithm
137
11.5
Quantum factorization
140
11.5.1
Factorization
141
11.5.2
The quantum Fourier transform
142
11.5.3
Phase estimation
144
11.6
Summary
145
12
Entanglement, computation and quantum measurements
146
12.1
Optimization of searches using entanglement
147
12.2
Model for quantum measurement
149
12.3
Correlations and quantum measurement
151
12.4
The ultimate limits of computation: the Bekenstein bound
157
12.5
Summary
158
13
Quantum error correction
160
13.1
Introduction
160
13.2
A simple example
160
χ
CONTENTS
13.3
General conditions
162
13.4
Reliable
quantum
computation
165
13.5
Quantum
error
correction
considered as a Maxwell's demon
167
13.5.1
Pure states
171
13.5.2
Mixed states
172
13.6
Summary
173
14
Outlook
175
Bibliography
179
Index
181 |
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| index_date | 2024-07-02T16:25:13Z |
| indexdate | 2024-07-09T20:52:20Z |
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| series2 | Oxford graduate texts |
| spelling | Vedral, Vlatko Verfasser (DE-588)141133368 aut Introduction to quantum information science Vlatko Vedral 1. publ. Oxford [u.a.] Oxford Univ. Press 2006 X, 183 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Quantencomputer - Quantenkommunikation Quantentheorie Quantum communication Quantum theory Quanteninformatik (DE-588)4705961-8 gnd rswk-swf (DE-588)4006432-3 Bibliografie gnd-content Quanteninformatik (DE-588)4705961-8 s DE-604 http://www.loc.gov/catdir/toc/fy0705/2007270101.html Inhaltsverzeichnis http://www.loc.gov/catdir/enhancements/fy0723/2007270101-d.html Beschreibung für Leser Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015416657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vedral, Vlatko Introduction to quantum information science Quantencomputer - Quantenkommunikation Quantentheorie Quantum communication Quantum theory Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4705961-8 (DE-588)4006432-3 |
| title | Introduction to quantum information science |
| title_auth | Introduction to quantum information science |
| title_exact_search | Introduction to quantum information science |
| title_exact_search_txtP | Introduction to quantum information science |
| title_full | Introduction to quantum information science Vlatko Vedral |
| title_fullStr | Introduction to quantum information science Vlatko Vedral |
| title_full_unstemmed | Introduction to quantum information science Vlatko Vedral |
| title_short | Introduction to quantum information science |
| title_sort | introduction to quantum information science |
| topic | Quantencomputer - Quantenkommunikation Quantentheorie Quantum communication Quantum theory Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Quantencomputer - Quantenkommunikation Quantentheorie Quantum communication Quantum theory Quanteninformatik Bibliografie |
| url | http://www.loc.gov/catdir/toc/fy0705/2007270101.html http://www.loc.gov/catdir/enhancements/fy0723/2007270101-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015416657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT vedralvlatko introductiontoquantuminformationscience |
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Inhaltsverzeichnis