Statistical structure of quantum theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Series: | Lecture notes in physics
New series M, monographs ; 67 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 159 S. graph. Darst. |
| ISBN: | 3540420827 9783642075629 |
Staff View
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Record in the Search Index
| _version_ | 1817681129620111360 |
|---|---|
| adam_text |
CONTENTS 0. INTRODUCTION .
1 0.1 FINITE DIMENSIONAL SYSTEMS . 1 0.2
GENERAL POSTULATES OF STATISTICAL DESCRIPTION . 3 0.3
CLASSICAL AND QUANTUM SYSTEMS . 4 0.4
RANDOMIZATION IN CLASSICAL AND QUANTUM STATISTICS . 5 0.5 CONVEX
GEOMETRY AND FUNDAMENTAL LIMITS FOR QUANTUM MEASUREMENTS
. 6 0.6 THE CORRESPONDENCE PROBLEM
. 8 0.7 REPEATED AND CONTINUOUS MEASUREMENTS
. 8 0.8 IRREVERSIBLE DYNAMICS
. 10 0.9 QUANTUM STOCHASTIC PROCESSES
. 11 1. THE STANDARD STATISTICAL MODEL
OFQUANTUM MECHANICS . 13 1.1 BASIC
CONCEPTS . 13 1.1.1 OPERATORS IN
HILBERT SPACE . 13 1.1.2 DENSITY OPERATORS
. 15 1.1.3 THE SPECTRAL MEASURE
. 16 1.1.4 THE STATISTICAL POSTULATE
. 17 1.1.5 COMPATIBLE OBSERVABLES
. 18 1.1.6 THE SIMPLEST QUANTUM SYSTEM
. 20 1.2 SYMMETRIES, KINEMATICS, DYNAMICS
. 22 1.2.1 GROUPS OF SYMMETRIES
. 22 1.2.2 ONE-PARAMETER
GROUPS. 23 1.2.3 THE WEYL RELATIONS
. 24 1.2.4 GAUSSIAN STATES
. 27 1.3 COMPOSITE SYSTEMS
. 29 1.3.1 THE TENSOR PRODUCT OF
HILBERT SPACES. 29 1.3.2 PRODUCT STATES
. 30 1.4 THE PROBLEM OFHIDDEN
VARIABLES . 31 1.4.1 HIDDEN VARIABLES AND
QUANTUM COMPLEMENTARITY . 31 1.4.2 HIDDEN VARIABLES AND QUANTUM
NONSEPARABILITY . 33 1.4.3 THE STRUCTURE OF THE SET OFQUANTUM
CORRELATIONS . 36 VIII CONTENTS 2. STATISTICS OF QUANTUM MEASUREMENTS
. 39 2.1 GENERALIZED OBSERVABLES
. 39 2.1.1 RESOLUTIONS OF THE
IDENTITY. 39 2.1.2 THE GENERALIZED STATISTICAL
MODEL OFQUANTUM MECHANICS . 41 2.1.3 THE
GEOMETRY OF THE SET OF GENERALIZED OBSERVABLES. . 43 2.2' QUANTUM
STATISTICAL DECISION THEORY . 45 2.2.1 OPTIMAL
DETECTION . 45 2.2.2 THE BAYES PROBLEM
. 47 2.2.3 THE QUANTUM CODING THEOREM
. 50 2.2.4 GENERAL FORMULATION
. 53 2.2.5 THE QUANTUM CRAM6R-RAO
INEQUALITIES . 56 2.2.6 RECENT PROGRESS IN STATE ESTIMATION
. 59 2.3 COVARIANT OBSERVABLES
. 61 2.3.1 FORMULATION OF THE PROBLEM
. 61 2.3.2 THE STRUCTURE OF A COVARIANT RESOLUTION
OF THE IDENTITY 62 2.3.3 GENERALIZED IMPRIMITIVITY SYSTEMS
. 64 2.3.4 THE CASE OF AN ABELIAN GROUP
. 65 2.3.5 CANONICAL CONJUGACY IN QUANTUM MECHANICS
. 67 2.3.6 LOCALIZABILITY . 70
3. EVOLUTION OFAN OPEN SYSTEM . 71 3.1
TRANSFORMATIONS OFQUANTUM STATES AND OBSERVABLES
. 71 3.1.1 COMPLETELY POSITIVE
MAPS . 71 3.1.2 OPERATIONS, DYNAMICAL MAPS
. 73 3.1.3
EXPECTATIONS. 75 3.2 QUANTUM CHANNEL
CAPACITIES . 76 3.2.1 THE NOTION OF CHANNEL
. 76 3.2.2 THE VARIETY OF CLASSICAL
CAPACITIES . 77 3.2.3 QUANTUM MUTUAL INFORMATION
. 79 3.2.4 THE QUANTUM CAPACITY
. 80 3.3 QUANTUM DYNAMICAL SEMIGROUPS
. 81 3.3.1 DEFINITION AND EXAMPLES
. 81 3.3.2 THE GENERATOR
. 83 3.3.3 UNBOUNDED GENERATORS
. 85 3.3.4 COVARIANT EVOLUTIONS
. 88 3.3.5 ERGODIC PROPERTIES .
. 91 3.3.6 DILATIONS OF DYNAMICAL SEMIGROUPS
. 93 4. REPEATED AND CONTINUOUS MEASUREMENT PROCESSES
. 97 4.1 STATISTICS OF REPEATED
MEASUREMENTS . 97 4.1.1 THE CONCEPT OF INSTRUMENT
. 97 4.1.2 REPRESENTATION OF A COMPLETELY
POSITIVE INSTRUMENT . 100 CONTENTS IX 4.1.3 THREE LEVELS OF DESCRIPTION
OFQUANTUM MEASUREMENTS 102 4.1.4 REPEATABILITY
. 103 4.1.5 MEASUREMENTS OF
CONTINUOUS OBSERVABLES . 105 4.1.6 THE STANDARD QUANTUM LIMIT
. 106 4.2 CONTINUOUS MEASUREMENT PROCESSES
. 108 4.2.1 NONDEMOLITION MEASUREMENTS
. 108 4.2.2 THE QUANTUM ZENO PARADOX
. 109 4.2.3 THE LIMIT THEOREM FOR CONVOLUTIONS OF
INSTRUMENTS . . 111 4.2.4 CONVOLUTION SEMIGROUPS OF INSTRUMENTS
. 113 4.2.5 INSTRUMENTAL PROCESSES
. 115 5. PROCESSES IN FOCK SPACE
. 119 5.1 QUANTUM STOCHASTIC CALCULUS
. 119 5.1.1 BASIC DEFINITIONS
. 119 5.1.2 THE STOCHASTIC INTEGRAL
. 121 5.1.3 THE QUANTUM ITO FORMULA
. 124 5.1.4 QUANTUM STOCHASTIC DIFFERENTIAL
EQUATIONS . 126 5.2 DILATIONS IN THE FOCK SPACE
. 130 5.2.1 WIENER AND POISSON PROCESSES IN
THE FOCK SPACE . 130 5.2.2 STOCHASTIC EVOLUTIONS AND DILATIONS OF
DYNAMICAL SEMIGROUPS . 133 5.2.3 DILATIONS OF
INSTRUMENTAL PROCESSES . 136 5.2.4 STOCHASTIC
REPRESENTATIONS OF CONTINUOUS MEASUREMENT PROCESSES . 138
5.2.5 NONLINEAR STOCHASTIC EQUATIONS OF POSTERIOR DYNAMICS 140
BIBLIOGRAPHY . 145
INDEX . 157 |
| any_adam_object | 1 |
| author | Cholevo, Aleksandr S. 1943- |
| author_GND | (DE-588)12282735X |
| author_facet | Cholevo, Aleksandr S. 1943- |
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| author_variant | a s c as asc |
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| ctrlnum | (OCoLC)248354896 (DE-599)BVBBV013703145 |
| discipline | Physik |
| format | Book |
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| spelling | Cholevo, Aleksandr S. 1943- Verfasser (DE-588)12282735X aut Statistical structure of quantum theory Alexander S. Holevo Berlin [u.a.] Springer 2001 IX, 159 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics : New series M, monographs 67 Physics and astronomy online library Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Quantenstatistik (DE-588)4047991-2 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Messprozess (DE-588)4169530-6 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Quantenstatistik (DE-588)4047991-2 s Messprozess (DE-588)4169530-6 s 1\p DE-604 Statistisches Modell (DE-588)4121722-6 s 2\p DE-604 Lecture notes in physics New series M, monographs ; 67 (DE-604)BV021852221 67 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009365601&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 | Cholevo, Aleksandr S. 1943- Statistical structure of quantum theory Lecture notes in physics Statistisches Modell (DE-588)4121722-6 gnd Quantenstatistik (DE-588)4047991-2 gnd Quantenmechanik (DE-588)4047989-4 gnd Messprozess (DE-588)4169530-6 gnd |
| subject_GND | (DE-588)4121722-6 (DE-588)4047991-2 (DE-588)4047989-4 (DE-588)4169530-6 |
| title | Statistical structure of quantum theory |
| title_auth | Statistical structure of quantum theory |
| title_exact_search | Statistical structure of quantum theory |
| title_full | Statistical structure of quantum theory Alexander S. Holevo |
| title_fullStr | Statistical structure of quantum theory Alexander S. Holevo |
| title_full_unstemmed | Statistical structure of quantum theory Alexander S. Holevo |
| title_short | Statistical structure of quantum theory |
| title_sort | statistical structure of quantum theory |
| topic | Statistisches Modell (DE-588)4121722-6 gnd Quantenstatistik (DE-588)4047991-2 gnd Quantenmechanik (DE-588)4047989-4 gnd Messprozess (DE-588)4169530-6 gnd |
| topic_facet | Statistisches Modell Quantenstatistik Quantenmechanik Messprozess |
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