Introduction to quantum information science:
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| Format: | Book |
|---|---|
| Language: | English Japanese |
| Published: |
Berlin [u.a.]
Springer
2015
|
| Series: | Graduate texts in physics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIV, 332 S. Ill., graph. Darst. |
| ISBN: | 9783662435014 3662435012 9783662435021 |
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Record in the Search Index
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CONTENTS
1 INVITATION TO QUANTUM INFORMATION SCIENCE 1
1.1 FROM CLASSICAL INFORMATION SCIENCE TO QUANTUM
INFORMATION SCIENCE 1
1.2 FURTHER EXPANSION OF QUANTUM INFORMATION SCIENCE 4
1.3 FEEDBACK FROM QUANTUM INFORMATION SCIENCE TO PHYSICS 6
1.4 TOWARD REALIZATION OF QUANTUM INFORMATION PROCESSING 8
1.5 ORGANIZATION OF THIS BOOK 9
REFERENCES 12
2 QUANTUM MECHANICS FOR QUBIT SYSTEMS 13
2.1 PRELIMINARY 13
2.2 PREPARATION 15
2.2.1 CONCEPTUAL PREPARATION: PHYSICAL SYSTEM, STATE,
MEASUREMENT OF PHYSICAL QUANTITY 15
2.2.2 NOTATIONAL PREPARATION: DIRAC NOTATION 16
2.3 QUBIT SYSTEMS 20
2.3.1 A QUBIT SYSTEM 21
2.3.2 TIME EVOLUTION IN QUBIT SYSTEM 24
2.3.3 COMPOSITION OF QUBIT SYSTEMS: N-QUBIT SYSTEMS 28
REFERENCES 34
3 FOUNDATIONS ON QUANTUM COMPUTING 37
3.1 WHAT IS COMPUTATION? 37
3.2 MATHEMATICAL NOTATION FOR INFORMATION SCIENCE 40
3.3 CLASSICAL CIRCUIT MODEL 41
3.4 QUANTUM CIRCUIT MODEL 45
REFERENCES 53
4 QUANTUM ALGORITHMS 55
4.1 INTRODUCTION 55
4.2 DEUTSCH-JOZSA ALGORITHM 56
XI
HTTP://D-NB.INFO/1050177967
XII CONTENTS
4.3 GRAVER'S ALGORITHM 59
4.3.1 CONSTRUCTION OF GRAVER'S ALGORITHM 59
4.3.2 ANALYSIS OF SUCCESS PROBABILITY 62
4.3.3 GENERALIZATION: MULTIPLE SOLUTIONS 64
4.4 SHOR'S ALGORITHM 66
4.4.1 QUANTUM ALGORITHM FOR PERIOD FINDING 66
4.4.2 QUANTUM ALGORITHM FOR FACTORIZATION 70
4.4.3 QUANTUM ALGORITHM FOR DISCRETE LOGARITHM 72
4.5 OTHER QUANTUM ALGORITHMS 73
REFERENCES 73
5 FOUNDATIONS OF QUANTUM MECHANICS AND QUANTUM
INFORMATION THEORY 75
5.1 INTRODUCTION 75
5.1.1 POSTULATES AND PRECONDITIONS 76
5.1.2 HILBERT SPACE AND LINEAR OPERATORS 77
5.1.3 DIRAC NOTATION II 78
5.2 POSTULATES FOR QUANTUM MECHANICS 80
5.2.1 QUANTUM STATES, AND MEASUREMENTS
OF PHYSICAL QUANTITIES 81
5.2.2 TIME EVOLUTION 88
5.2.3 COMPOSITE SYSTEMS 89
5.2.4 COMMENT ON THE MEASUREMENT PROCESS:
STATE-CHANGES DUE TO MEASUREMENTS 91
5.3 REFORMULATION OF QUANTUM MECHANICS 93
5.3.1 GENERAL CLASS OF QUANTUM STATES 93
5.3.2 GENERAL CLASS OF MEASUREMENTS 107
5.3.3 GENERAL CLASS OF TIME EVOLUTIONS 115
5.3.4 GENERAL CLASS OF MEASUREMENT PROCESSES 119
REFERENCES 125
6 INFORMATION QUANTITIES IN QUANTUM SYSTEMS 127
6.1 INTRODUCTION 127
6.2 INFORMATION QUANTITIES IN CLASSICAL SYSTEMS 128
6.2.1 SHANNON ENTROPY 128
6.2.2 ENTROPY AND TYPICAL SEQUENCE 130
6.2.3 JOINT ENTROPY AND CONDITIONAL ENTROPY 134
6.2.4 CONDITIONAL PROBABILITY AND CLASSICAL CHANNEL 135
6.2.5 DIVERGENCE 136
6.2.6 /-DIVERGENCE 138
6.2.7 MUTUAL INFORMATION 141
6.2.8 CONCAVITY AND SUBADDITIVITY OF THE ENTROPY 143
6.2.9 FANO INEQUALITY 144
CONTENTS XIII
6.3 INFORMATION QUANTITIES IN QUANTUM SYSTEMS 145
6.3.1 VON NEUMANN ENTROPY 145
6.3.2 QUANTUM RELATIVE ENTROPY 147
6.3.3 MUTUAL INFORMATION IN QUANTUM SYSTEMS 149
6.3.4 CONCAVITY AND SUBADDITIVITY OF THE VON NEUMANN
ENTROPY 152
6.3.5 TRACE DISTANCE 153
6.3.6 FIDELITY AND UHLMANN'S THEOREM 155
6.3.7 PROPERTIES OF FIDELITY 158
6.3.8 ENTANGLEMENT FIDELITY 162
REFERENCES 165
7 QUANTUM ENTANGLEMENT 167
7.1 INTRODUCTION 167
7.2 BASIC CONCEPTS OF ENTANGLEMENT 168
7.2.1 QUANTUM AND CLASSICAL CORRELATION 168
7.2.2 PRODUCT STATE AND MAXIMALLY ENTANGLED STATE 169
7.2.3 QUANTUM TELEPORTATION 171
7.2.4 SUPERDENSE CODING 173
7.3 QUANTIFYING ENTANGLEMENT 174
7.3.1 LOCAL OPERATIONS AND CLASSICAL
COMMUNICATION (LOCC) 174
7.3.2 BASIC UNIT OF ENTANGLEMENT 176
7.3.3 ENTANGLEMENT CONCENTRATION 177
7.3.4 QUANTUM DATA COMPRESSION 180
7.3.5 ENTANGLEMENT DILUTION 183
7.3.6 AMOUNT OF ENTANGLEMENT 185
7.4 MULTIPARTITE ENTANGLEMENT 186
7.4.1 GHZ AND W STATE 186
7.4.2 STOCHASTIC LOCC 187
7.4.3 CLASSIFICATION OF MULTIPARTITE ENTANGLEMENT 188
7.5 MIXED-STATE ENTANGLEMENT 190
7.5.1 ENTANGLEMENT CRITERIA 190
7.5.2 LOCC ON MIXED STATES 194
7.5.3 ENTANGLEMENT MEASURE 196
7.5.4 ENTANGLEMENT OF FORMATION 197
7.5.5 RELATIVE ENTROPY OF ENTANGLEMENT 199
7.5.6 RELATIONSHIP AMONG ENTANGLEMENT MEASURES 200
7.5.7 ENTANGLEMENT MONOTONE 202
REFERENCES 202
8 CLASSICAL-QUANTUM CHANNEL CODING 205
8.1 INTRODUCTION 205
8.2 QUANTUM HYPOTHESIS TESTING 206
XIV CONTENTS
8.2.1 PROBLEM OF QUANTUM HYPOTHESIS TESTING 206
8.2.2 TRACE INEQUALITY FOR QUANTUM HYPOTHESIS TESTING 208
8.2.3 ASYMPTOTIC THEORY OF QUANTUM HYPOTHESIS TESTING . . 210
8.2.4 PROPERTIES OF RELATIVE RENYI ENTROPY 213
8.3 CLASSICAL-QUANTUM CHANNEL CODING 216
8.3.1 MESSAGE TRANSMISSION OVER QUANTUM CHANNELS 216
8.3.2 PROOF OF THE C-Q CHANNEL CODING THEOREM
(CONVERSE PART) 219
8.3.3 PROOF OF THE C-Q CHANNEL CODING THEOREM
(DIRECT PART) 223
REFERENCES 228
9 QUANTUM ERROR CORRECTION AND QUANTUM CRYPTOGRAPHY 231
9.1 INTRODUCTION 231
9.2 ALGEBRAIC ERROR CORRECTION IN THE CLASSICAL SYSTEM 232
9.2.1 FORMULATION 232
9.2.2 EVALUATION OF ERROR PROBABILITY UNDER CODE
ENSEMBLE 236
9.2.3 EXAMPLES OF CODE ENSEMBLE 239
9.2.4 ASYMPTOTIC THEORY 241
9.2.5 ERROR CORRECTION WITH CONFIDENTIALITY 242
9.3 QUANTUM ERROR CORRECTING CODE 246
9.3.1 PAULI CHANNEL 246
9.3.2 STABILIZER CODE 247
9.3.3 CSS CODE 250
9.3.4 ASYMPTOTIC THEORY 254
9.4 APPLICATION TO QUANTUM SECRET COMMUNICATION 255
9.4.1 CHANNEL TO THE ENVIRONMENT SYSTEM 255
9.4.2 LEAKED INFORMATION WITHOUT PRIVACY AMPLIFICATION . 256
9.4.3 LEAKED INFORMATION WITH PRIVACY AMPLIFICATION 260
9.5 APPLICATION TO QUANTUM CRYPTOGRAPHY
(QUANTUM KEY DISTRIBUTION) 264
REFERENCES 268
APPENDIX A: FOUNDATIONS OF LINEAR ALGEBRA
AND BASIC MATHEMATICS 269
APPENDIX B: SOLUTION FOR EXERCISES 305
INDEX 327 |
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| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik |
| format | Book |
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| spelling | Ryoushi Jouhou Kagaku Nyuumon Introduction to quantum information science Masahito Hayashi ... Berlin [u.a.] Springer 2015 XIV, 332 S. Ill., 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 Hayashi, Masahito 1971- Sonstige (DE-588)131819313 oth X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4644268&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027524780&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Introduction to quantum information science Quanteninformatik (DE-588)4705961-8 gnd |
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| title | Introduction to quantum information science |
| title_alt | Ryoushi Jouhou Kagaku Nyuumon |
| title_auth | Introduction to quantum information science |
| title_exact_search | Introduction to quantum information science |
| title_full | Introduction to quantum information science Masahito Hayashi ... |
| title_fullStr | Introduction to quantum information science Masahito Hayashi ... |
| title_full_unstemmed | Introduction to quantum information science Masahito Hayashi ... |
| title_short | Introduction to quantum information science |
| title_sort | introduction to quantum information science |
| topic | Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Quanteninformatik |
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