Quantum information: an overview
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2007
|
| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [249]-270) and index |
| Physical Description: | XVIII, 284 S. Ill. |
| ISBN: | 0387357254 9780387357256 |
Staff View
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Record in the Search Index
| _version_ | 1804136414996070400 |
|---|---|
| adam_text | Contents
Foreword
......................................................
vii
Preface
........................................................ xi
Acknowledgments
............................................. xiii
1
Qubits
..................................................... 1
1.1
Quantum state purity
.................................... 5
1.2
The representation of qubits
.............................. 8
1.3
Stokes parameters
....................................... 11
1.4
Single-qubit gates
....................................... 14
1.5
The double-slit experiment
............................... 18
1.6
The Mach-Zehnder interferometer
......................... 23
1.7
Quantum coherence and information processing
............. 25
2
Measurements and quantum operations
.................... 29
2.1
The
von
Neumann classification of processes
................ 32
2.2
The
Pauli
classification of measurements
................... 34
2.3
Expectation values and the
von
Neumann projection
......... 35
2.4
The
Lüders
rule
......................................... 37
2.5
Reduced statistical operators
.............................. 38
2.6
General quantum operations
.............................. 39
2.7
Positive-operator-valued measures
......................... 41
3
Quantum nonlocality and
interferometry
.................. 45
3.1
Hidden variables and state completeness
.................... 46
3.2 Von
Neumann s no-go theorem
.......................... 48
3.3
The Einstein-Podolsky-Rosen argument
.................... 49
3.4
Gleason s theorem
....................................... 51
3.5
Bell inequalities
......................................... 52
3.6
Interferometrie
complementarity
........................... 57
xvi Contents
3.7
The Pranson interferometer
............................... 61
3.8
Two-qubit quantum gates
................................ 63
4
Classical information and communication
.................. 67
4.1
Communication channels
................................. 68
4.2
Shannon entropy
........................................ 70
4.3
Rényi
entropy
........................................... 74
4.4
Coding
................................................. 74
4.5
Error correction
......................................... 77
4.6
Data compression
....................................... 78
4.7
Communication complexity
............................... 79
5
Quantum information
...................................... 81
5.1
Quantum entropy
....................................... 82
5.2
Quantum relative and conditional entropies
................. 84
5.3
Quantum mutual information
............................. 85
5.4
Fidelity and coherent information
......................... 86
5.5
Quantum
Rényi
and Tsallis entropies
...................... 88
6
Quantum entanglement
.................................... 91
6.1
Basic definitions
......................................... 92
6.2
The Schmidt decomposition
............................... 94
6.3
Special bases and decompositions
.......................... 95
6.4
Stokes parameters and entanglement
....................... 98
6.5
Partial transpose and reduction criteria
.................... 99
6.6
The fundamental postulate
.............................101
6.7
Entanglement monotones
.................................102
6.8
Distillation and bound entanglement
.......................104
6.9
Entanglement and majorization
...........................105
6.10
Concurrence
............................................106
6.11
Entanglement witnesses
..................................107
6.12
Entanglement as a resource
...............................108
6.13
The thermodynamic analogy
..............................109
6.14
Information and the foundations of physics
.................112
6.15
The geometry of entanglement
............................114
6.16
Creating entangled photons
...............................115
7
Entangled multipartite systems
............................121
7.1
Stokes and correlation tensors
.............................124
7.2
JV-tangle
................................................126
7.3
Generalized Schmidt decomposition
........................127
7.4
Lorentz-group isometries
.................................127
7.5
Entanglement classes
....................................129
7.6
Algebraic invariants of multipartite systems
.................131
7.7
Three-qubit states and residual tangle
......................133
Contents xvii
7.8 Three-qubit
quantum
logic gates
..........................135
7.9
States of higher qubit number
.............................136
8
Quantum state and process estimation
.....................139
8.1
Quantum state tomography
...............................140
8.2
Quantum process tomography
.............................143
8.3
Direct estimation methods
................................144
9
Quantum communication
..................................147
9.1
Quantum channels
.......................................148
9.2
Quantum channel capacities
..............................149
9.3
Holevo s theorem
........................................151
9.4
Discrimination of quantum states
..........................153
9.5
The no-cloning theorem
..................................156
9.6
Basic quantum channels
..................................157
9.7
The GHJW theorem
.....................................159
9.8
Quantum dense coding
...................................160
9.9
Quantum
teleportation
...................................162
9.10
Entanglement swapping
................................164
9.11
Entanglement purification
..............................165
9.12
Quantum data compression
...............................167
9.13
Quantum communication complexity
.......................169
10
Quantum decoherence and its mitigation
..................171
10.1
Quantum decoherence
....................................172
10.2
Decoherence and mixtures
................................173
10.3
Decoherence-free subspaces
...............................174
10.4
Quantum coding, error detection, and correction
............175
10.5
The nine-qubit Shor code
.................................179
10.6
Stabilizer codes
.........................................181
10.7
Concatenation of quantum codes
..........................183
11
Quantum broadcasting, copying, and deleting
..............185
11.1
Quantum broadcasting
...................................185
11.2
Quantum copying
.......................................186
11.3
Quantum deleting
.......................................189
11.4
Landauer s principle
.....................................190
12
Quantum key distribution
.................................191
12.1
Cryptography and cryptosystems
..........................191
12.2
QKD systems
...........................................193
12.3
The BB84 (four-state) protocol
............................195
12.4
The E91 (Ekert) protocol
.................................197
12.5
The B92 (two-state) protocol
.............................198
12.6
The six-state protocol
....................................199
xviii Contents
12.7
Eavesdropping
..........................................199
12.8
Security proofs
..........................................201
13
Classical and quantum computing
.........................203
13.1
Classical computing and computational complexity
..........204
13.2
Deterministic Turing machines
............................206
13.3
Probabilistic Turing machines
.............................207
13.4
Multi-tape Turing machines
...............................208
13.5
Quantum Turing machines
................................209
13.6
Quantum computational complexity
.......................211
13.7
Fault-tolerant quantum computing
.........................214
13.8
Linear optical quantum computation
.......................215
14
Quantum algorithms
.......................................219
14.1
The Deutsch-Jozsa algorithm
.............................220
14.2
The
Grover
search algorithm
..............................221
14.3
The Shor factoring algorithm
.............................224
14.4
The Simon algorithm
....................................229
A Mathematical elements
....................................231
A.I Boolean algebra and Galois fields
.........................231
A.2 Random variables
.......................................232
A.3 Vector Spaces and Hubert space
...........................233
A.4 The standard quantum formalism
.........................237
A.5 The Dirac notation
......................................237
A.6 Groups of transformations
................................239
A.7 Probability, lattices, and posets
...........................240
A.8 Projectors, correlations, and the Kochen-Specker theorem
.... 242
A.9 Traditional quantum logic
................................243
В
The quantum postulates
...................................245
B.I The standard postulates
..................................245
B.2 The
Heisenberg-Robertson
uncertainty relation
.............247
B.3 Liouville space and open quantum systems
..................248
References
.....................................................249
Index
..........................................................271
|
| adam_txt |
Contents
Foreword
.
vii
Preface
. xi
Acknowledgments
. xiii
1
Qubits
. 1
1.1
Quantum state purity
. 5
1.2
The representation of qubits
. 8
1.3
Stokes parameters
. 11
1.4
Single-qubit gates
. 14
1.5
The double-slit experiment
. 18
1.6
The Mach-Zehnder interferometer
. 23
1.7
Quantum coherence and information processing
. 25
2
Measurements and quantum operations
. 29
2.1
The
von
Neumann classification of processes
. 32
2.2
The
Pauli
classification of measurements
. 34
2.3
Expectation values and the
von
Neumann projection
. 35
2.4
The
Lüders
rule
. 37
2.5
Reduced statistical operators
. 38
2.6
General quantum operations
. 39
2.7
Positive-operator-valued measures
. 41
3
Quantum nonlocality and
interferometry
. 45
3.1
Hidden variables and state completeness
. 46
3.2 Von
Neumann's "no-go" theorem
. 48
3.3
The Einstein-Podolsky-Rosen argument
. 49
3.4
Gleason's theorem
. 51
3.5
Bell inequalities
. 52
3.6
Interferometrie
complementarity
. 57
xvi Contents
3.7
The Pranson interferometer
. 61
3.8
Two-qubit quantum gates
. 63
4
Classical information and communication
. 67
4.1
Communication channels
. 68
4.2
Shannon entropy
. 70
4.3
Rényi
entropy
. 74
4.4
Coding
. 74
4.5
Error correction
. 77
4.6
Data compression
. 78
4.7
Communication complexity
. 79
5
Quantum information
. 81
5.1
Quantum entropy
. 82
5.2
Quantum relative and conditional entropies
. 84
5.3
Quantum mutual information
. 85
5.4
Fidelity and coherent information
. 86
5.5
Quantum
Rényi
and Tsallis entropies
. 88
6
Quantum entanglement
. 91
6.1
Basic definitions
. 92
6.2
The Schmidt decomposition
. 94
6.3
Special bases and decompositions
. 95
6.4
Stokes parameters and entanglement
. 98
6.5
Partial transpose and reduction criteria
. 99
6.6
The "fundamental postulate"
.101
6.7
Entanglement monotones
.102
6.8
Distillation and bound entanglement
.104
6.9
Entanglement and majorization
.105
6.10
Concurrence
.106
6.11
Entanglement witnesses
.107
6.12
Entanglement as a resource
.108
6.13
The thermodynamic analogy
.109
6.14
Information and the foundations of physics
.112
6.15
The geometry of entanglement
.114
6.16
Creating entangled photons
.115
7
Entangled multipartite systems
.121
7.1
Stokes and correlation tensors
.124
7.2
JV-tangle
.126
7.3
Generalized Schmidt decomposition
.127
7.4
Lorentz-group isometries
.127
7.5
Entanglement classes
.129
7.6
Algebraic invariants of multipartite systems
.131
7.7
Three-qubit states and residual tangle
.133
Contents xvii
7.8 Three-qubit
quantum
logic gates
.135
7.9
States of higher qubit number
.136
8
Quantum state and process estimation
.139
8.1
Quantum state tomography
.140
8.2
Quantum process tomography
.143
8.3
Direct estimation methods
.144
9
Quantum communication
.147
9.1
Quantum channels
.148
9.2
Quantum channel capacities
.149
9.3
Holevo's theorem
.151
9.4
Discrimination of quantum states
.153
9.5
The no-cloning theorem
.156
9.6
Basic quantum channels
.157
9.7
The GHJW theorem
.159
9.8
Quantum dense coding
.160
9.9
Quantum
teleportation
.162
9.10
Entanglement "swapping"
.164
9.11
Entanglement "purification"
.165
9.12
Quantum data compression
.167
9.13
Quantum communication complexity
.169
10
Quantum decoherence and its mitigation
.171
10.1
Quantum decoherence
.172
10.2
Decoherence and mixtures
.173
10.3
Decoherence-free subspaces
.174
10.4
Quantum coding, error detection, and correction
.175
10.5
The nine-qubit Shor code
.179
10.6
Stabilizer codes
.181
10.7
Concatenation of quantum codes
.183
11
Quantum broadcasting, copying, and deleting
.185
11.1
Quantum broadcasting
.185
11.2
Quantum copying
.186
11.3
Quantum deleting
.189
11.4
Landauer's principle
.190
12
Quantum key distribution
.191
12.1
Cryptography and cryptosystems
.191
12.2
QKD systems
.193
12.3
The BB84 (four-state) protocol
.195
12.4
The E91 (Ekert) protocol
.197
12.5
The B92 (two-state) protocol
.198
12.6
The six-state protocol
.199
xviii Contents
12.7
Eavesdropping
.199
12.8
Security proofs
.201
13
Classical and quantum computing
.203
13.1
Classical computing and computational complexity
.204
13.2
Deterministic Turing machines
.206
13.3
Probabilistic Turing machines
.207
13.4
Multi-tape Turing machines
.208
13.5
Quantum Turing machines
.209
13.6
Quantum computational complexity
.211
13.7
Fault-tolerant quantum computing
.214
13.8
Linear optical quantum computation
.215
14
Quantum algorithms
.219
14.1
The Deutsch-Jozsa algorithm
.220
14.2
The
Grover
search algorithm
.221
14.3
The Shor factoring algorithm
.224
14.4
The Simon algorithm
.229
A Mathematical elements
.231
A.I Boolean algebra and Galois fields
.231
A.2 Random variables
.232
A.3 Vector Spaces and Hubert space
.233
A.4 The standard quantum formalism
.237
A.5 The Dirac notation
.237
A.6 Groups of transformations
.239
A.7 Probability, lattices, and posets
.240
A.8 Projectors, correlations, and the Kochen-Specker theorem
. 242
A.9 Traditional quantum logic
.243
В
The quantum postulates
.245
B.I The standard postulates
.245
B.2 The
Heisenberg-Robertson
uncertainty relation
.247
B.3 Liouville space and open quantum systems
.248
References
.249
Index
.271 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Jaeger, Gregg |
| author_GND | (DE-588)139170464 |
| author_facet | Jaeger, Gregg |
| author_role | aut |
| author_sort | Jaeger, Gregg |
| author_variant | g j gj |
| building | Verbundindex |
| bvnumber | BV022364872 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.889 |
| callnumber-search | QA76.889 |
| callnumber-sort | QA 276.889 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 152 UK 1000 UK 1200 UK 2000 |
| ctrlnum | (OCoLC)77793646 (DE-599)BVBBV022364872 |
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| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004 |
| dewey-search | 004 |
| dewey-sort | 14 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik |
| discipline_str_mv | Physik Informatik |
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| id | DE-604.BV022364872 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:04:50Z |
| indexdate | 2024-07-09T20:56:02Z |
| institution | BVB |
| isbn | 0387357254 9780387357256 |
| language | English |
| lccn | 2006928325 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015574147 |
| oclc_num | 77793646 |
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| owner_facet | DE-706 DE-1051 DE-634 DE-83 DE-11 DE-355 DE-BY-UBR |
| physical | XVIII, 284 S. Ill. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Jaeger, Gregg Verfasser (DE-588)139170464 aut Quantum information an overview Gregg Jaeger New York Springer 2007 XVIII, 284 S. Ill. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. [249]-270) and index Quantum computers Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 s DE-604 Quantencomputer (DE-588)4533372-5 s http://deposit.dnb.de/cgi-bin/dokserv?id=2820413&prov=M&dok_var=1&dok_ext=htm 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=015574147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jaeger, Gregg Quantum information an overview Quantum computers Quantencomputer (DE-588)4533372-5 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4533372-5 (DE-588)4705961-8 |
| title | Quantum information an overview |
| title_auth | Quantum information an overview |
| title_exact_search | Quantum information an overview |
| title_exact_search_txtP | Quantum information an overview |
| title_full | Quantum information an overview Gregg Jaeger |
| title_fullStr | Quantum information an overview Gregg Jaeger |
| title_full_unstemmed | Quantum information an overview Gregg Jaeger |
| title_short | Quantum information |
| title_sort | quantum information an overview |
| title_sub | an overview |
| topic | Quantum computers Quantencomputer (DE-588)4533372-5 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Quantum computers Quantencomputer Quanteninformatik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2820413&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015574147&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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