Entangled systems: new directions in quantum physics
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| Sprache: | English German |
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Weinheim
WILEY-VCH
2007
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| Beschreibung: | XVII, 338 S. Ill., graph. Darst. |
| ISBN: | 9783527406845 3527406840 |
Internformat
MARC
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| 100 | 1 | |a Audretsch, Jürgen |d 1942- |e Verfasser |0 (DE-588)120727706 |4 aut | |
| 240 | 1 | 0 | |a Verschränkte Systeme - die Quantenphysik auf neuen Wegen |
| 245 | 1 | 0 | |a Entangled systems |b new directions in quantum physics |c Jürgen Audretsch |
| 264 | 1 | |a Weinheim |b WILEY-VCH |c 2007 | |
| 300 | |a XVII, 338 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 0 | 7 | |a Verschränkter Zustand |0 (DE-588)4409616-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1805088838984400896 |
|---|---|
| adam_text |
Contents
Preface
to the English Edition
XIII
Preface to the German Edition XV
1
The Mathematical Framework
1
1.1
Hubert Vector Space
. 2
1.1.1
The Scalar Product and the Dirac Notation
. 2
1.1.2
Linear Operators on the Hubert Space
. 3
1. ] .3
Normal Operators and Spectral Decompositions
. 6
1.1.4
Hermitian Operators
. 9
1.1.5
Unitary Operators
. 11
1.1.6
Positive Operators and Projection Operators
. 11
1.2
Liouville Operator Space
. 13
1.2.1
Scalar Product
. 13
1.2.2
Superoperators
. 14
1.3
The Elements of Probability Theory
. 15
1.3.1
The Probability of Random Events
. 15
1.3.2
Conditional Probability and
Bayes'
Theorem
. 17
1.3.3
Random Quantities
. 19'
1.4
Complementary Topics and Further Reading
. 19
1.5
Problems for Chapter
1. 20
2
Basic Concepts of Quantum Theory
23
2.1
First Version of the Postulates (pure states of isolated quantum systems)
. 23
2.1.1
Introduction: the Scenario of Quantum Mechanics
. 23
2.1.2
Quantum States
. 29
2.1.3
Postulates for Pure States of Isolated Quantum Systems
. 32
2.1.4
Comments on the Postulates
. 35
2.2
Outlook
. 37
2.3
Manipulation of the Evolution of the States by
Projective
Measurements
. 38
2.3.1
The Quantum
Zeno
Effect
. 38
2.3.2
Driving a State Vector by a Sequence of Projection Measurements
. . 39
2.4
The Structure of Physical Theories*
. 40
Contents
2
АЛ
Structural
Elements
of a Physical Theory*
. 41
2.4.2
Developed Reality*
. 42
2.5
Interpretations of Quantum Theory and Physical Reality*
. 43
2.5.1
The Minimal Interpretation*
. 43
2.5.2
The Standard Interpretation*
. 44
2.6
Complementary Topics and Further Reading
. 46
The Simplest Quantum Systems: Qubits
49
3.1 Pauli
Operators
. 50
3.2
Visualisation of Qubits on the Bloch Sphere
. 52
3.3
Visualisation of the Measurement Dynamics and the Unitary Dynamics
. 55
3.4
Quantum Gates for Single Qubit Systems
. 59
3.5
Spin-ì
.
62
3.6
Photon Polarisations
. 62
3.7
Single Photons in a Beam Splitter and in an Interferometer
. 63
3.7.1
Beamsplitters
. 64
3.7.2
Interferometer
. 66
3.8
Locating a Bomb Without Exploding It by Using a Null Measurement*
. 68
3.9
Complementary Topics and Further Reading
. 71
3.10
Problems for Chapter
3. 71
Mixed States and the Density Operator
73
4.1
Density Operators for a Given Ensemble (Statistical Mixture)
. 73
4.1.1
Pure States
. 73
4.1.2
The Physics of Statistical MiKtures (Blends)
. 75
4.1.3
Definition and Properties of the Generalised Density Operator
. 78
4.1.4
Incoherent Superpositions of Pure States
. 80
4.2
The Generalised Quantum State
. 82
4.3
Different Ensemble Decompositions of a Density Operator and the Ignorance
Interpretation
. 82
4.4
Density Operators of Qubits
. 85
4.5
Complementary Topics and Further Reading
. 86
4.6
Problems for Chapter
4. 86
Shannon's Entropy and Classical Information
89
5.1
Definition and Properties
. 89
5.2
Shannon^ Theorem
. 93
5.2.1
Typical Sequences
. 93
5.2.2
Classical Data Compression
. 95
5.3
Classical Information
. 96
5.4
Classical Relative Entropy
. 97
5.5
Mutual Information as a Measure of the Correlation between Two Messages
. 97
5.5.1
Mutual Information
. 98
5.5.2
Conditional Entropy
. 99
5.6
Complementary Topics and Further Reading
. 101
5.7
Problems for Chapter
5. 101
Contents
VII
6
The von
Neumann Entropy and Quantum Information
103
6.1
The Quantum Channel and Quantum Entropy
. 103
6.2
Qubits as the Unit of Quantum Information
. 106
6.3
Properties
. 108
6.4
The Interfaces of Preparation and Measurement
. 110
6.4.1
The Entropy of
Projective
Measurements
. 110
6.4.2
The Entropy of Preparation
.
Ill
6.5
Quantum Information
. 112
6.6
Complementary Topics and Further Reading
. 112
6.7
Problems for Chapter
6. 113
7
Composite Systems
115
7.1
Subsystems
. 115
7.2
The Product Hubert Space
. 116
7.2.1
Vectors
. 116
7.2.2
Operators
. 118
7.3
The Fundamentals of the Physics of Composite Quantum Systems
. 120
7.3.1
Postulates for Composite Systems and Outlook
. 120
7.3.2
The State of a Subsystem, the Reduced Density Operator, and General
Mixtures
. 122
7.4
Manipulations on a Subsystem
. 124
7.4.1
Relative States and Local Unitary Transformations
. 124
7.4.2
Selective Local Measurements
. 125
7.4.3
A Non-Selective Local Measurement
. 127
7.5
Separate Manipulations on both Subsystems
. 128
7.5.1
Pairs of Selective Measurements
. 128
7.5.2
Non-Local Effects: "Spooky Action at a Distance"?
. 130
7.6
The Unitary Dynamics of Composite Systems
. 131
7.7
A First Application of Entanglement: a Conjuring Trick
. 132
7.7.1
The Conjuring Trick
. 132
7.7.2
Classical Correlations can give no Explanation
. 133
7.7.3
The Trick
. 134
7.8
Quantum Gates for Multiple Qubit Systems
. 135
7.8.1
Entanglement via
a CNOT
Gate
. 135
7.8.2
Toffoli, SWAP, and
Deutsch
Gates
. 137
7.9
Systems of Identical Particles"
. 138
7.10
Complementary Topics and Further Reading
. 141
7.11
Problems for Chapter
7. 142
8
Entanglement
143
8.1
Correlations and Entanglement
. 143
8.1.1
Classically-Correlated Quantum States and LOCC
. 143
8.1.2
Separability and Entanglement
. 145
8.1.3
The Separability Problem
. 147
8.2
Outlook
. 148
VIII Contents
8.3
Entangled
Pure States
. 149
8.3.1
The Schmidt Decomposition
. 149
8.3.2
The Schmidt Number and Entanglement
. 151
8.3.3
The Entropy of the Subsystems as a Measure of Entanglement
. 152
8.3.4
Subsystems in Pure States are not Entangled*
. 153
8.4
The PPT Criterion for the Entanglement of Mixtures
* . 155
8.5
The Production of Entangled States
. 157
8.6
The No-Cloning Theorem Prevents Transfer of Information Faster than the
Velocity of Light
. 159
8.7
Marking States by Entanglement*
. 161
8.7.1
Which-Way Marking*
. 161
8.7.2
Quantum Erasure*
. 164
8.7.3
Delayed Choice of the Marker
Observables*
. 165
8.8
Complementary Topics and Further Reading
. 166
8.9
Problems for Chapter
8. 167
9
Correlations and Non-Local Measurements
169
9.1
Entropies and the Correlations of Composite Quantum Systems
. 169
9.1.1
Mutual Information as a Measure of Correlations
. 169
9.1.2
The Triangle Inequality
. 170
9.1.3
Entangled
ví.
Classically-Correlated Quantum Systems
. 171
9.2
Non-Local Measurements
. 174
9.2.1
The Bell Basis
. 174
9.2.2
Local and Non-Local Measurements
. 175
9.2.3
Non-local Measurements by Means of Local Measurements on an An¬
cillary System
. 177
9.2.4
Non-locally Stored Information and Bell Measurements
. 179
9.3
Complementary Topics and Further Reading
. 181
9.4
Problems for Chapter
9. 181
10
There is no (Local-Realistic) Alternative to Quantum Theory
183
10.1
EPR Experiments and Their Quantum-mechanical Explanation
. 183
10.2
Correlated Gloves
. 186
10.3
Local Realism
. 187
10.4
Hidden Variables. Bell Inequalities and Contradictions of Experiments
. 188
10.5
Separable Mixtures Obey the Bell Inequality
. 191
10.6
Entanglement Witnesses*
. 192
10.7
3-Partiele Entanglement and Quantum Locality
. 194
10.7.1
The GHZ State
. 194
10.7.2
Local Realism and Quantum Theory at Odds
. 194
10.8
Complementary Topics and Further Reading
. 196
10.9
Problems for Chapter
10. 197
Contents
IX
11
Working with Entanglement
199
11.1
Quantum Cryptography
. 199
11.1.1
The
Vernam
Coding
. 199
11.1.2
The B92 Protocol
. 200
11.1.3
EPR Protocols
. 202
11.1.4
The Scheme of Quantum Cryptography
. 203
11.2
One Qubit Transmits Two Bits (Dense Coding)
. 204
11.3
Quantum
Teleportation
. 204
1
1.4
Entanglement Swapping
. 207
1
1.5
Spooky Action into the Past?*
. 208
6
Entanglement Distillation
. 209
[ 1.7
A Measure of Entanglement for Mixtures: Entanglement of Formation and
Concurrence*
. 212
[1.8
Complementary Topics and Further Reading
. 216
Ì1.9
Problems for Chapter
11 . 217
12
The Quantum Computer
219
12.1
Registers and Networks
. 219
12.2
Functional Computation
. 221
12.3
Quantum Parallelism
. 224
12.4
Two Simple Quantum Algorithms
. 225
12.4.1
The
Deutsch
Problem
. 225
12.4.2
The Deutsch-Jozsa Problem
. 226
12.5
Grover's Search Algorithm
. 228
12.6
Shor's Factorisation Algorithm
. 230
12.6.1
Reduction of Factorisation to the Search for a Period
. 231
12.6.2
The Quantum Algorithm for Determining the Period
. 234
12.7
Quantum Error Correction Using Non-local Measurements
. 239
12.7.1
Bit Flip Errors
. 239
12.7.2
Phase Flip Errors
. 240
12.8
The Components of the Quantum Computer*
. 241
12.9
Complementary Topics and Further Reading
. 243
12.
lOProblems for Chapter
12. 244
13
Generalised Measurements, POVM
247
13.1
The Function of a Generalised Dynamics of Open Quantum Systems
. 247
13.1.1
Problems
. 247
13.1.2
A Simple Example
. 248
13.2
The Non-optimal Stern-Gerlach Experiment and Generalised Measurements
. 251
13.2.1
The Experimental Setup
. 251
13.2.2
An Example of a Generalised Measurement
. 253
13.2.3
Unsharp Measurements
. 255
13.3
Generalised Measurements
. 256
13.3.1
What is a Quantum Measurement?
. 256
13.3.2
Generalised Measurement Postulates
. 257
χ
Contents
13.3.3
The Polar Decomposition of
a
Linear Operator. 258
13.3.4
Minimal Measurements and POVM
. 260
13.3.5
Implementation of a Generalised Measurement by Unitary Transfor¬
mation and Projection
. 261
13.3.6
Entanglement Distillation by means of Generalised Measurements*
. 262
13.4
POVM Measurements
. 263
13.4.1
Measurement Probabilities and Positive Operators
. 263
13.4.2
A Composite Measurement as an Example of a POVM Measurement
264
13.4.3
Can One Distinguish Between Two States with Certainty by a Single
POVM Measurement?
. 265
13.4.4
The Advantage of a POVM Measurement for Determining States
. . 267
13.4.5
An Informationally-Complete POVM*
. 268
13.4.6
Estimating the State Before the Measurement
. 269
13.5
Complementary Topics and Further Reading
. 270
13.6
Problems for Chapter
13. 270
14
The General Evolution of an Open Quantum System and Special Quantum Chan¬
nels
273
14.1
Quantum Operations and their Operator-Sum Decompositions
. 273
14.1.1
Quantum Operations
. 273
14.1.2
The Operator-Sum Decomposition of Quantum Operations
. 275
14.1.3
Simple Quantum Operations
. 276
14.1.4
The Ambiguity of the Operator-Sum Decomposition
. 277
14.2
The Master Equation
. 277
14.3
Completely General Selective Measurements and POVM
. 279
14.4
Quantum Channels
. 281
14.4.1
The Depolarising Channel
. 281
14.4.2
Quantum Jumps and Amplitude Damping Channels
. 282
14.4.3
An Entanglement-Breaking Channel
*. 283
14.5
The Scenario and the Rules of Quantum Theory Revisited
. 284
14.6
Complementary Topics and Further Reading
. 288
14.7
Problems for Chapter
14. 288
15
Decoherence and Approaches to the Description of the Quantum Measurement
Process
289
15.1
Channels which Produce Decoherence
. 289
15.1.1
The Phase Damping Channel
. 289
15.1.2
Scattering and Decoherence
. 291
15.1.3
The Phase Flip Channel
. 292
15.2
Environment-Induced Decoherence
. 293
15.2.1
The Formation of the Classical World
. 293
15.2.2 Schrödinger's
Cat
. 296
15.3
The Quantum Measurement Process*
. 297
15.3.1
The Research Programme*
. 297
15.3.2
Pre-Measurement"
. 298
Contents
XI
15.3.3
Entanglement with the
Environment Fixes
the
Observable*
. 299
15.3.4
Entanglement with Many Degrees of Freedom of the Environment*
. 300
15.4
Has the Problem of Measurements been Solved?*
. 303
15.5
The Many-Worlds Interpretation*
. 303
15.6
Complementary Topics and Further Reading
. 304
15.7
Problems for Chapter
15 . 306
16
Two Implementations of Quantum Operations*
307
16.1
The Operator-Sum Decomposition*
. 307
16.2
The Unitary Implementation of Quantum Operations*
. 310
16.3
Implementation of a Completely General Selective Measurement by Unitary
Transformation and Projection*
. 311
16.4
Complementary Topics and Further Reading*
. 313
16.5
Problems for Chapter
16 . 313
References
315
Reference categories
. 315
Bibliography
. 316
Subject Index
331 |
| adam_txt |
Contents
Preface
to the English Edition
XIII
Preface to the German Edition XV
1
The Mathematical Framework
1
1.1
Hubert Vector Space
. 2
1.1.1
The Scalar Product and the Dirac Notation
. 2
1.1.2
Linear Operators on the Hubert Space
. 3
1. ] .3
Normal Operators and Spectral Decompositions
. 6
1.1.4
Hermitian Operators
. 9
1.1.5
Unitary Operators
. 11
1.1.6
Positive Operators and Projection Operators
. 11
1.2
Liouville Operator Space
. 13
1.2.1
Scalar Product
. 13
1.2.2
Superoperators
. 14
1.3
The Elements of Probability Theory
. 15
1.3.1
The Probability of Random Events
. 15
1.3.2
Conditional Probability and
Bayes'
Theorem
. 17
1.3.3
Random Quantities
. 19'
1.4
Complementary Topics and Further Reading
. 19
1.5
Problems for Chapter
1. 20
2
Basic Concepts of Quantum Theory
23
2.1
First Version of the Postulates (pure states of isolated quantum systems)
. 23
2.1.1
Introduction: the Scenario of Quantum Mechanics
. 23
2.1.2
Quantum States
. 29
2.1.3
Postulates for Pure States of Isolated Quantum Systems
. 32
2.1.4
Comments on the Postulates
. 35
2.2
Outlook
. 37
2.3
Manipulation of the Evolution of the States by
Projective
Measurements
. 38
2.3.1
The Quantum
Zeno
Effect
. 38
2.3.2
Driving a State Vector by a Sequence of Projection Measurements
. . 39
2.4
The Structure of Physical Theories*
. 40
Contents
2
АЛ
Structural
Elements
of a Physical Theory*
. 41
2.4.2
Developed Reality*
. 42
2.5
Interpretations of Quantum Theory and Physical Reality*
. 43
2.5.1
The Minimal Interpretation*
. 43
2.5.2
The Standard Interpretation*
. 44
2.6
Complementary Topics and Further Reading
. 46
The Simplest Quantum Systems: Qubits
49
3.1 Pauli
Operators
. 50
3.2
Visualisation of Qubits on the Bloch Sphere
. 52
3.3
Visualisation of the Measurement Dynamics and the Unitary Dynamics
. 55
3.4
Quantum Gates for Single Qubit Systems
. 59
3.5
Spin-ì
.
62
3.6
Photon Polarisations
. 62
3.7
Single Photons in a Beam Splitter and in an Interferometer
. 63
3.7.1
Beamsplitters
. 64
3.7.2
Interferometer
. 66
3.8
Locating a Bomb Without Exploding It by Using a Null Measurement*
. 68
3.9
Complementary Topics and Further Reading
. 71
3.10
Problems for Chapter
3. 71
Mixed States and the Density Operator
73
4.1
Density Operators for a Given Ensemble (Statistical Mixture)
. 73
4.1.1
Pure States
. 73
4.1.2
The Physics of Statistical MiKtures (Blends)
. 75
4.1.3
Definition and Properties of the Generalised Density Operator
. 78
4.1.4
Incoherent Superpositions of Pure States
. 80
4.2
The Generalised Quantum State
. 82
4.3
Different Ensemble Decompositions of a Density Operator and the Ignorance
Interpretation
. 82
4.4
Density Operators of Qubits
. 85
4.5
Complementary Topics and Further Reading
. 86
4.6
Problems for Chapter
4. 86
Shannon's Entropy and Classical Information
89
5.1
Definition and Properties
. 89
5.2
Shannon^ Theorem
. 93
5.2.1
Typical Sequences
. 93
5.2.2
Classical Data Compression
. 95
5.3
Classical Information
. 96
5.4
Classical Relative Entropy
. 97
5.5
Mutual Information as a Measure of the Correlation between Two Messages
. 97
5.5.1
Mutual Information
. 98
5.5.2
Conditional Entropy
. 99
5.6
Complementary Topics and Further Reading
. 101
5.7
Problems for Chapter
5. 101
Contents
VII
6
The von
Neumann Entropy and Quantum Information
103
6.1
The Quantum Channel and Quantum Entropy
. 103
6.2
Qubits as the Unit of Quantum Information
. 106
6.3
Properties
. 108
6.4
The Interfaces of Preparation and Measurement
. 110
6.4.1
The Entropy of
Projective
Measurements
. 110
6.4.2
The Entropy of Preparation
.
Ill
6.5
Quantum Information
. 112
6.6
Complementary Topics and Further Reading
. 112
6.7
Problems for Chapter
6. 113
7
Composite Systems
115
7.1
Subsystems
. 115
7.2
The Product Hubert Space
. 116
7.2.1
Vectors
. 116
7.2.2
Operators
. 118
7.3
The Fundamentals of the Physics of Composite Quantum Systems
. 120
7.3.1
Postulates for Composite Systems and Outlook
. 120
7.3.2
The State of a Subsystem, the Reduced Density Operator, and General
Mixtures
. 122
7.4
Manipulations on a Subsystem
. 124
7.4.1
Relative States and Local Unitary Transformations
. 124
7.4.2
Selective Local Measurements
. 125
7.4.3
A Non-Selective Local Measurement
. 127
7.5
Separate Manipulations on both Subsystems
. 128
7.5.1
Pairs of Selective Measurements
. 128
7.5.2
Non-Local Effects: "Spooky Action at a Distance"?
. 130
7.6
The Unitary Dynamics of Composite Systems
. 131
7.7
A First Application of Entanglement: a Conjuring Trick
. 132
7.7.1
The Conjuring Trick
. 132
7.7.2
Classical Correlations can give no Explanation
. 133
7.7.3
The Trick
. 134
7.8
Quantum Gates for Multiple Qubit Systems
. 135
7.8.1
Entanglement via
a CNOT
Gate
. 135
7.8.2
Toffoli, SWAP, and
Deutsch
Gates
. 137
7.9
Systems of Identical Particles"
. 138
7.10
Complementary Topics and Further Reading
. 141
7.11
Problems for Chapter
7. 142
8
Entanglement
143
8.1
Correlations and Entanglement
. 143
8.1.1
Classically-Correlated Quantum States and LOCC
. 143
8.1.2
Separability and Entanglement
. 145
8.1.3
The Separability Problem
. 147
8.2
Outlook
. 148
VIII Contents
8.3
Entangled
Pure States
. 149
8.3.1
The Schmidt Decomposition
. 149
8.3.2
The Schmidt Number and Entanglement
. 151
8.3.3
The Entropy of the Subsystems as a Measure of Entanglement
. 152
8.3.4
Subsystems in Pure States are not Entangled*
. 153
8.4
The PPT Criterion for the Entanglement of Mixtures
* . 155
8.5
The Production of Entangled States
. 157
8.6
The No-Cloning Theorem Prevents Transfer of Information Faster than the
Velocity of Light
. 159
8.7
Marking States by Entanglement*
. 161
8.7.1
Which-Way Marking*
. 161
8.7.2
Quantum Erasure*
. 164
8.7.3
Delayed Choice of the Marker
Observables*
. 165
8.8
Complementary Topics and Further Reading
. 166
8.9
Problems for Chapter
8. 167
9
Correlations and Non-Local Measurements
169
9.1
Entropies and the Correlations of Composite Quantum Systems
. 169
9.1.1
Mutual Information as a Measure of Correlations
. 169
9.1.2
The Triangle Inequality
. 170
9.1.3
Entangled
ví.
Classically-Correlated Quantum Systems
. 171
9.2
Non-Local Measurements
. 174
9.2.1
The Bell Basis
. 174
9.2.2
Local and Non-Local Measurements
. 175
9.2.3
Non-local Measurements by Means of Local Measurements on an An¬
cillary System
. 177
9.2.4
Non-locally Stored Information and Bell Measurements
. 179
9.3
Complementary Topics and Further Reading
. 181
9.4
Problems for Chapter
9. 181
10
There is no (Local-Realistic) Alternative to Quantum Theory
183
10.1
EPR Experiments and Their Quantum-mechanical Explanation
. 183
10.2
Correlated Gloves
. 186
10.3
Local Realism
. 187
10.4
Hidden Variables. Bell Inequalities and Contradictions of Experiments
. 188
10.5
Separable Mixtures Obey the Bell Inequality
. 191
10.6
Entanglement Witnesses*
. 192
10.7
3-Partiele Entanglement and Quantum Locality
. 194
10.7.1
The GHZ State
. 194
10.7.2
Local Realism and Quantum Theory at Odds
. 194
10.8
Complementary Topics and Further Reading
. 196
10.9
Problems for Chapter
10. 197
Contents
IX
11
Working with Entanglement
199
11.1
Quantum Cryptography
. 199
11.1.1
The
Vernam
Coding
. 199
11.1.2
The B92 Protocol
. 200
11.1.3
EPR Protocols
. 202
11.1.4
The Scheme of Quantum Cryptography
. 203
11.2
One Qubit Transmits Two Bits (Dense Coding)
. 204
11.3
Quantum
Teleportation
. 204
1
1.4
Entanglement Swapping
. 207
1
1.5
Spooky Action into the Past?*
. 208
6
Entanglement Distillation
. 209
[ 1.7
A Measure of Entanglement for Mixtures: Entanglement of Formation and
Concurrence*
. 212
[1.8
Complementary Topics and Further Reading
. 216
Ì1.9
Problems for Chapter
11 . 217
12
The Quantum Computer
219
12.1
Registers and Networks
. 219
12.2
Functional Computation
. 221
12.3
Quantum Parallelism
. 224
12.4
Two Simple Quantum Algorithms
. 225
12.4.1
The
Deutsch
Problem
. 225
12.4.2
The Deutsch-Jozsa Problem
. 226
12.5
Grover's Search Algorithm
. 228
12.6
Shor's Factorisation Algorithm
. 230
12.6.1
Reduction of Factorisation to the Search for a Period
. 231
12.6.2
The Quantum Algorithm for Determining the Period
. 234
12.7
Quantum Error Correction Using Non-local Measurements
. 239
12.7.1
Bit Flip Errors
. 239
12.7.2
Phase Flip Errors
. 240
12.8
The Components of the Quantum Computer*
. 241
12.9
Complementary Topics and Further Reading
. 243
12.
lOProblems for Chapter
12. 244
13
Generalised Measurements, POVM
247
13.1
The Function of a Generalised Dynamics of Open Quantum Systems
. 247
13.1.1
Problems
. 247
13.1.2
A Simple Example
. 248
13.2
The Non-optimal Stern-Gerlach Experiment and Generalised Measurements
. 251
13.2.1
The Experimental Setup
. 251
13.2.2
An Example of a Generalised Measurement
. 253
13.2.3
Unsharp Measurements
. 255
13.3
Generalised Measurements
. 256
13.3.1
What is a Quantum Measurement?
. 256
13.3.2
Generalised Measurement Postulates
. 257
χ
Contents
13.3.3
The Polar Decomposition of
a
Linear Operator. 258
13.3.4
Minimal Measurements and POVM
. 260
13.3.5
Implementation of a Generalised Measurement by Unitary Transfor¬
mation and Projection
. 261
13.3.6
Entanglement Distillation by means of Generalised Measurements*
. 262
13.4
POVM Measurements
. 263
13.4.1
Measurement Probabilities and Positive Operators
. 263
13.4.2
A Composite Measurement as an Example of a POVM Measurement
264
13.4.3
Can One Distinguish Between Two States with Certainty by a Single
POVM Measurement?
. 265
13.4.4
The Advantage of a POVM Measurement for Determining States
. . 267
13.4.5
An Informationally-Complete POVM*
. 268
13.4.6
Estimating the State Before the Measurement
. 269
13.5
Complementary Topics and Further Reading
. 270
13.6
Problems for Chapter
13. 270
14
The General Evolution of an Open Quantum System and Special Quantum Chan¬
nels
273
14.1
Quantum Operations and their Operator-Sum Decompositions
. 273
14.1.1
Quantum Operations
. 273
14.1.2
The Operator-Sum Decomposition of Quantum Operations
. 275
14.1.3
Simple Quantum Operations
. 276
14.1.4
The Ambiguity of the Operator-Sum Decomposition
. 277
14.2
The Master Equation
. 277
14.3
Completely General Selective Measurements and POVM
. 279
14.4
Quantum Channels
. 281
14.4.1
The Depolarising Channel
. 281
14.4.2
Quantum Jumps and Amplitude Damping Channels
. 282
14.4.3
An Entanglement-Breaking Channel
*. 283
14.5
The Scenario and the Rules of Quantum Theory Revisited
. 284
14.6
Complementary Topics and Further Reading
. 288
14.7
Problems for Chapter
14. 288
15
Decoherence and Approaches to the Description of the Quantum Measurement
Process
289
15.1
Channels which Produce Decoherence
. 289
15.1.1
The Phase Damping Channel
. 289
15.1.2
Scattering and Decoherence
. 291
15.1.3
The Phase Flip Channel
. 292
15.2
Environment-Induced Decoherence
. 293
15.2.1
The Formation of the Classical World
. 293
15.2.2 Schrödinger's
Cat
. 296
15.3
The Quantum Measurement Process*
. 297
15.3.1
The Research Programme*
. 297
15.3.2
Pre-Measurement"
. 298
Contents
XI
15.3.3
Entanglement with the
Environment Fixes
the
Observable*
. 299
15.3.4
Entanglement with Many Degrees of Freedom of the Environment*
. 300
15.4
Has the Problem of Measurements been Solved?*
. 303
15.5
The Many-Worlds Interpretation*
. 303
15.6
Complementary Topics and Further Reading
. 304
15.7
Problems for Chapter
15 . 306
16
Two Implementations of Quantum Operations*
307
16.1
The Operator-Sum Decomposition*
. 307
16.2
The Unitary Implementation of Quantum Operations*
. 310
16.3
Implementation of a Completely General Selective Measurement by Unitary
Transformation and Projection*
. 311
16.4
Complementary Topics and Further Reading*
. 313
16.5
Problems for Chapter
16 . 313
References
315
Reference categories
. 315
Bibliography
. 316
Subject Index
331 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Audretsch, Jürgen 1942- |
| author_GND | (DE-588)120727706 |
| author_facet | Audretsch, Jürgen 1942- |
| author_role | aut |
| author_sort | Audretsch, Jürgen 1942- |
| author_variant | j a ja |
| building | Verbundindex |
| bvnumber | BV022367979 |
| classification_rvk | UH 5600 UK 1000 |
| ctrlnum | (OCoLC)180726665 (DE-599)BVBBV022367979 |
| 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 |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV022367979 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:05:54Z |
| indexdate | 2024-07-20T09:14:23Z |
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| isbn | 9783527406845 3527406840 |
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| physical | XVII, 338 S. Ill., graph. Darst. |
| publishDate | 2007 |
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| series2 | Physics textbook |
| spelling | Audretsch, Jürgen 1942- Verfasser (DE-588)120727706 aut Verschränkte Systeme - die Quantenphysik auf neuen Wegen Entangled systems new directions in quantum physics Jürgen Audretsch Weinheim WILEY-VCH 2007 XVII, 338 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Quantenphysik (DE-588)4266670-3 gnd rswk-swf Verschränkter Zustand (DE-588)4409616-1 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Verschränkter Zustand (DE-588)4409616-1 s DE-604 Quantenmechanik (DE-588)4047989-4 s Quantenphysik (DE-588)4266670-3 s 1\p DE-604 Quantentheorie (DE-588)4047992-4 s 2\p DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2909697&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015577207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Audretsch, Jürgen 1942- Entangled systems new directions in quantum physics Quantenphysik (DE-588)4266670-3 gnd Verschränkter Zustand (DE-588)4409616-1 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4266670-3 (DE-588)4409616-1 (DE-588)4047992-4 (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Entangled systems new directions in quantum physics |
| title_alt | Verschränkte Systeme - die Quantenphysik auf neuen Wegen |
| title_auth | Entangled systems new directions in quantum physics |
| title_exact_search | Entangled systems new directions in quantum physics |
| title_exact_search_txtP | Entangled systems new directions in quantum physics |
| title_full | Entangled systems new directions in quantum physics Jürgen Audretsch |
| title_fullStr | Entangled systems new directions in quantum physics Jürgen Audretsch |
| title_full_unstemmed | Entangled systems new directions in quantum physics Jürgen Audretsch |
| title_short | Entangled systems |
| title_sort | entangled systems new directions in quantum physics |
| title_sub | new directions in quantum physics |
| topic | Quantenphysik (DE-588)4266670-3 gnd Verschränkter Zustand (DE-588)4409616-1 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenphysik Verschränkter Zustand Quantentheorie Quantenmechanik Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2909697&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=015577207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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