Quantum systems, channels, information: a mathematical introduction
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2019]
|
| Edition: | 2nd edition |
| Series: | Texts and monographs in theoretical physics
|
| Subjects: | |
| Online Access: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110642247&searchTitles=true Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XV, 350 Seiten Illustrationen |
| ISBN: | 9783110642247 3110642247 |
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MARC
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| 100 | 1 | |a Cholevo, Aleksandr S. |d 1943- |e Verfasser |0 (DE-588)12282735X |4 aut | |
| 245 | 1 | 0 | |a Quantum systems, channels, information |b a mathematical introduction |c Alexander S. Holevo |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a Berlin |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XV, 350 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts and monographs in theoretical physics | |
| 650 | 0 | 7 | |a Quanteninformatik |0 (DE-588)4705961-8 |2 gnd |9 rswk-swf |
| 653 | |a Quantenkanal | ||
| 653 | |a Quantencomputer | ||
| 653 | |a Quanteninformatik | ||
| 653 | |a Quantum Computing; Quantum Cryptography; Quantum Information; Quantum Systems; Quantum Theory | ||
| 653 | |a Quantum Systems | ||
| 653 | |a Quantum Cryptography | ||
| 653 | |a Quantum Computing | ||
| 653 | |a Quantum Information | ||
| 653 | |a Quantum Theory | ||
| 689 | 0 | 0 | |a Quanteninformatik |0 (DE-588)4705961-8 |D s |
| 689 | 0 | |5 DE-604 | |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe,(PDF) |z 9783110642490 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-031544615 | ||
Record in the Search Index
| _version_ | 1804180517554225152 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
V
PREFACE
TO
THE
SECOND
EDITION
*
IX
PART
I:
BASIC
STRUCTURES
1
1.1
1.2
1.3
1.4
1.5
1.6
VECTORS
AND
OPERATORS
*
3
HILBERT
SPACE
*
3
OPERATORS
*
4
POSITIVITY
*
5
TRACE
AND
DUALITY
*
6
CONVEXITY
*
7
NOTES
AND
REFERENCES
*
8
2
2.1
2.1.1
2.1.2
2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.4
2.4.1
2.4.2
2.5
STATES,
OBSERVABLES,
STATISTICS
*
10
STRUCTURE
OF
STATISTICAL
THEORIES
*
10
CLASSICAL
SYSTEMS
*
10
AXIOMS
OF
STATISTICAL
DESCRIPTION
*
11
QUANTUM
STATES
*
13
QUANTUM
OBSERVABLES
*
16
QUANTUM
OBSERVABLES
FROM
THE
AXIOMS
*
16
COMPATIBILITY
AND
COMPLEMENTARITY
*
18
THE
UNCERTAINTY
RELATION
*
20
CONVEX
STRUCTURE
OF
OBSERVABLES
*
21
STATISTICAL
DISCRIMINATION
BETWEEN
QUANTUM
STATES
*
24
FORMULATION
OF
THE
PROBLEM
*
24
OPTIMAL
OBSERVABLES
*
25
NOTES
AND
REFERENCES
*
31
3
3.1
3.1.1
3.1.2
3.1.3
3.2
3.2.1
3.2.2
3.3
3.3.1
COMPOSITE
SYSTEMS
AND
ENTANGLEMENT
*
33
COMPOSITE
SYSTEMS
*
33
TENSOR
PRODUCTS
*
33
NAIMARK
*
S
DILATION
*
35
SCHMIDT
DECOMPOSITION
AND
PURIFICATION
*
37
QUANTUM
ENTANGLEMENT
VS.
*
LOCAL
REALISM
*
*
39
PARADOX
OF
EINSTEIN-PODOLSKI-ROSEN
AND
BELL
*
S
INEQUALITIES
*
39
MERMIN-PERES
GAME
*
43
QUANTUM
SYSTEMS
AS
INFORMATION
CARRIERS
*
45
TRANSMISSION
OF
CLASSICAL
INFORMATION
*
45
XII
*
CONTENTS
3.3.2
ENTANGLEMENT
AND
LOCAL
OPERATIONS
*
46
3.3.3
SUPERDENSE
CODING
*
47
3.3.4
QUANTUM
TELEPORTATION
*
48
3.4
NOTES
AND
REFERENCES
*
50
PART
II:
THE
PRIMARY
CODING
THEOREMS
4
CLASSICAL
ENTROPY
AND
INFORMATION
*
55
4.1
ENTROPY
OF
A
RANDOM
VARIABLE
AND
DATA
COMPRESSION
*
55
4.2
CONDITIONAL
ENTROPY
AND
THE
SHANNON
INFORMATION
*
57
4.3
THE
SHANNON
CAPACITY
OF
THE
CLASSICAL
NOISY
CHANNEL
*
60
4.4
THE
CHANNEL
CODING
THEOREM
*
61
4.5
WIRETAP
CHANNEL
*
67
4.6
GAUSSIAN
CHANNEL
*
68
4.7
NOTES
AND
REFERENCES
*
70
5
THE
CLASSICAL-QUANTUM
CHANNEL
*
71
5.1 CODES
AND
ACHIEVABLE
RATES
*
71
5.2
FORMULATION
OF
THE
CODING
THEOREM
-----
72
5.3
THE
UPPER
BOUND
*
75
5.4
PROOF
OF
THE
WEAK
CONVERSE
*
79
5.5
TYPICAL PROJECTORS
*
83
5.6
PROOF
OF
THE
DIRECT CODING
THEOREM
*
*
88
5.7
THE
RELIABILITY
FUNCTION
FOR
PURE-STATE
CHANNEL
*
90
5.8
NOTES
AND
REFERENCES
*
93
PART
III:
CHANNELS
AND
ENTROPIES
6
QUANTUM
EVOLUTIONS
AND
CHANNELS
*
99
6.1
QUANTUM
EVOLUTIONS
*
99
6.2
COMPLETELY
POSITIVE
MAPS
*
102
6.3
DEFINITION
OF
THE
CHANNEL
*
108
6.4
ENTANGLEMENT-BREAKING
AND
PPT
CHANNELS
*
110
6.5
QUANTUM
MEASUREMENT
PROCESSES
*
112
6.6
COMPLEMENTARY
CHANNELS
*
115
6.7
COVARIANT
CHANNELS
*
119
6.8
QUBIT
CHANNELS
*
122
6.9
NOTES
AND
REFERENCES
*
124
7
QUANTUM
ENTROPY
AND
INFORMATION
QUANTITIES
*
126
CONTENTS
*
XIII
7.1
QUANTUM
RELATIVE
ENTROPY
*
126
7.2
MONOTONICITY
OF
THE
RELATIVE
ENTROPY
*
127
7.3
STRONG
SUBADDITIVITY
OF
THE
QUANTUM
ENTROPY
*
132
7.4
CONTINUITY
PROPERTIES
*
134
7.5
INFORMATION
CORRELATION,
ENTANGLEMENT
OF
FORMATION,
AND
CONDITIONAL
ENTROPY
-----
136
7.6
ENTROPY
EXCHANGE
*
141
7.7
QUANTUM
MUTUAL
INFORMATION
*
142
7.8
NOTES
AND
REFERENCES
*
144
PART
IV:
BASIC
CHANNEL
CAPACITIES
8
THE
CLASSICAL
CAPACITY
OF
QUANTUM
CHANNELS
*
149
8.1
THE
CODING
THEOREM
*
149
8.2
THEX-CAPACITY
*
151
8.3
THE
ADDITIVITY
PROBLEM
*
154
8.3.1
THE
EFFECT
OF
ENTANGLEMENT
IN
ENCODING
AND
DECODING
*
154
8.3.2
A
HIERARCHY
OF
ADDITIVITY
PROPERTIES
*
157
8.3.3
SOME
ENTROPY
INEQUALITIES
*
160
8.3.4
ADDITIVITY
FOR
COMPLEMENTARY
CHANNELS
*
163
8.3.5
NONADDITIVITY
OF
QUANTUM
ENTROPY
QUANTITIES
*
164
8.4
NOTES
AND
REFERENCES
*
171
9
ENTANGLEMENT-ASSISTED
CLASSICAL
COMMUNICATION
*
173
9.1
THE
GAIN
OF
ENTANGLEMENT
ASSISTANCE
*
173
9.2
THE
CLASSICAL
CAPACITIES
OF
QUANTUM
OBSERVABLES
*
177
9.3
PROOF
OF
THE
CONVERSE
CODING
THEOREM
*
181
9.4
PROOF
OF
THE
DIRECT
CODING
THEOREM
*
183
9.5
NOTES
AND
REFERENCES
*
186
10
TRANSMISSION
OF
QUANTUM
INFORMATION
*
187
10.1
QUANTUM
ERROR-CORRECTING
CODES
*
187
10.1.1
ERROR
CORRECTION
BY
REPETITION
*
187
10.1.2
GENERAL
FORMULATION
*
189
10.1.3
NECESSARY
AND
SUFFICIENT
CONDITIONS
FOR
ERROR
CORRECTION
*
190
10.1.4
COHERENT
INFORMATION
AND
PERFECT
ERROR
CORRECTION
*
191
10.2
FIDELITIES
FOR
QUANTUM
INFORMATION
*
195
10.2.1
FIDELITIES
FOR
PURE
STATES
*
195
10.2.2
RELATIONS
BETWEEN
THE
FIDELITY
MEASURES
*
197
10.2.3
FIDELITY
AND
THE
BURES
DISTANCE
*
199
10.3
THE
QUANTUM
CAPACITY
*
202
XIV
*
CONTENTS
10.3.1
ACHIEVABLE
RATES
*
202
10.3.2
THE
QUANTUM
CAPACITY
AND
THE
COHERENT
INFORMATION
*
206
10.3.3
DEGRADABLE
CHANNELS
*
208
10.4
THE
PRIVATE
CLASSICAL
CAPACITY
AND
THE
QUANTUM
CAPACITY
*
211
10.4.1
THE
QUANTUM
WIRETAP
CHANNEL
*
211
10.4.2
PROOF
OF
THE
PRIVATE
CAPACITY
THEOREM
*
214
10.4.3
LARGE
DEVIATIONS
FOR
RANDOM
OPERATORS
*
220
10.4.4
THE
DIRECT CODING
THEOREM
FOR
THE
QUANTUM
CAPACITY
*
222
10.5
NOTES
AND
REFERENCES
*
227
PARTV:
INFINITE
SYSTEMS
11
CHANNELS
WITH
CONSTRAINED
INPUTS
*
233
11.1
CONVERGENCE
OF
DENSITY
OPERATORS
*
233
11.2
QUANTUM
ENTROPY
AND
RELATIVE
ENTROPY
*
237
11.3
CONSTRAINED
C-Q
CHANNEL
*
239
11.4
CLASSICAL-QUANTUM
CHANNEL
WITH
CONTINUOUS
ALPHABET
*
241
11.5
CONSTRAINED
QUANTUM
CHANNEL
*
243
11.6
ENTANGLEMENT-ASSISTED
CAPACITY
OF
CONSTRAINED
CHANNELS
*
247
11.7
ENTANGLEMENT-BREAKING
CHANNELS
IN
INFINITE
DIMENSIONS
*
248
11.8
NOTES
AND
REFERENCES
*
253
12
GAUSSIAN
SYSTEMS
*
255
12.1
PRELIMINARY
MATERIAL
*
255
12.1.1
SPECTRAL
DECOMPOSITION
AND
STONE
*
S
THEOREM
*
255
12.1.2
OPERATORS
ASSOCIATED
WITH
THE
HEISENBERG
COMMUTATION
RELATION
*
258
12.1.3
CLASSICAL
SIGNAL
PLUS
QUANTUM
NOISE
*
261
12.1.4
THE
CLASSICAL-QUANTUM
GAUSSIAN
CHANNEL
*
263
12.2
CANONICAL
COMMUTATION
RELATIONS
*
265
12.2.1
WEYL-SEGAL
CANONICAL
COMMUTATION
RELATION
*
265
12.2.2
THE
SYMPLECTIC
SPACE
*
267
12.2.3
DYNAMICS,
QUADRATIC
OPERATORS,
AND
GAUGE
TRANSFORMATIONS
*
269
12.3
GAUSSIAN
STATES
*
273
12.3.1
CHARACTERISTIC
FUNCTION
*
273
12.3.2
DEFINITION
AND
PROPERTIES
OF
GAUSSIAN
STATES
*
274
12.3.3
THE
DENSITY
OPERATOR
OF
GAUSSIAN
STATE
*
279
12.3.4
ENTROPY
OF
A
GAUSSIAN
STATE
*
281
12.3.5
SEPARABILITY
AND
PURIFICATION
*
284
12.4
GAUSSIAN
CHANNELS
*
287
12.4.1
OPEN
BOSONIC
SYSTEMS
*
287
CONTENTS
*
XV
12.4.2
GAUSSIAN
CHANNELS:
BASIC
PROPERTIES
*
291
12.4.3
GAUSSIAN
OBSERVABLES
*
292
12.4.4
GAUSSIAN
ENTANGLEMENT-BREAKING
CHANNELS
*
294
12.5
THE
CAPACITIES
OF
GAUSSIAN
CHANNELS
*
297
12.5.1
MAXIMIZATION
OF
THE
MUTUAL
INFORMATION
*
297
12.5.2
GAUGE
COVARIANT
CHANNELS
I
*
299
12.5.3
MAXIMIZATION
OF
THE
COHERENT
INFORMATION
*
301
12.5.4
THE
CLASSICAL
CAPACITY
*
302
12.6
THE
CASE
OF
SINGLE
MODE
-----
319
12.6.1
CLASSIFICATION
OF
GAUSSIAN
CHANNELS
*
319
12.6.2
ENTANGLEMENT-BREAKING
CHANNELS
*
324
12.6.3
ATTENUATION/AMPLIFICATION/CLASSICAL
NOISE
CHANNEL
*
325
12.6.4
ESTIMATING
THE
QUANTUM
CAPACITY
*
328
12.7
NOTES
AND
REFERENCES
*
333
BIBLIOGRAPHY
*
337
INDEX
*
348
|
| any_adam_object | 1 |
| author | Cholevo, Aleksandr S. 1943- |
| author_GND | (DE-588)12282735X |
| author_facet | Cholevo, Aleksandr S. 1943- |
| author_role | aut |
| author_sort | Cholevo, Aleksandr S. 1943- |
| author_variant | a s c as asc |
| building | Verbundindex |
| bvnumber | BV046164747 |
| classification_rvk | ST 152 UG 3000 UK 8000 |
| ctrlnum | (OCoLC)1112609130 (DE-599)DNB1183130562 |
| 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 Mathematik |
| edition | 2nd edition |
| format | Book |
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| id | DE-604.BV046164747 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:37:01Z |
| institution | BVB |
| isbn | 9783110642247 3110642247 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031544615 |
| oclc_num | 1112609130 |
| open_access_boolean | |
| owner | DE-11 DE-634 DE-20 |
| owner_facet | DE-11 DE-634 DE-20 |
| physical | XV, 350 Seiten Illustrationen |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | Texts and monographs in theoretical physics |
| spelling | Cholevo, Aleksandr S. 1943- Verfasser (DE-588)12282735X aut Quantum systems, channels, information a mathematical introduction Alexander S. Holevo 2nd edition Berlin De Gruyter [2019] © 2019 XV, 350 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Texts and monographs in theoretical physics Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Quantenkanal Quantencomputer Quanteninformatik Quantum Computing; Quantum Cryptography; Quantum Information; Quantum Systems; Quantum Theory Quantum Systems Quantum Cryptography Quantum Computing Quantum Information Quantum Theory Quanteninformatik (DE-588)4705961-8 s DE-604 Erscheint auch als Online-Ausgabe,(EPUB) 9783110642407 Erscheint auch als Online-Ausgabe,(PDF) 9783110642490 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110642247&searchTitles=true B:DE-101 application/pdf http://d-nb.info/1183130562/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031544615&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cholevo, Aleksandr S. 1943- Quantum systems, channels, information a mathematical introduction Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4705961-8 |
| title | Quantum systems, channels, information a mathematical introduction |
| title_auth | Quantum systems, channels, information a mathematical introduction |
| title_exact_search | Quantum systems, channels, information a mathematical introduction |
| title_full | Quantum systems, channels, information a mathematical introduction Alexander S. Holevo |
| title_fullStr | Quantum systems, channels, information a mathematical introduction Alexander S. Holevo |
| title_full_unstemmed | Quantum systems, channels, information a mathematical introduction Alexander S. Holevo |
| title_short | Quantum systems, channels, information |
| title_sort | quantum systems channels information a mathematical introduction |
| title_sub | a mathematical introduction |
| topic | Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Quanteninformatik |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110642247&searchTitles=true http://d-nb.info/1183130562/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031544615&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cholevoaleksandrs quantumsystemschannelsinformationamathematicalintroduction |
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