Entanglement properties of quantum states and quantum operations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Garching
MPQ
2003
|
| Edition: | Als Ms. des Autors gedr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Innsbruck, Univ., Diss., 2003 |
| Physical Description: | 247 S. graph. Darst. : 30 cm |
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MARC
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| 001 | BV017260796 | ||
| 003 | DE-604 | ||
| 005 | 20230704 | ||
| 007 | t | ||
| 008 | 030624s2003 gw d||| tm|| 00||| eng d | ||
| 016 | 7 | |a 967725844 |2 DE-101 | |
| 035 | |a (OCoLC)76507522 | ||
| 035 | |a (DE-599)BVBBV017260796 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-12 |a DE-19 | ||
| 088 | |a MPQ 282 | ||
| 100 | 1 | |a Kraus, Barbara |d 1975- |e Verfasser |0 (DE-588)1294886754 |4 aut | |
| 245 | 1 | 0 | |a Entanglement properties of quantum states and quantum operations |c eingereicht von Barbara Kraus. [Max-Planck-Institut für Quantenoptik] |
| 250 | |a Als Ms. des Autors gedr. | ||
| 264 | 1 | |a Garching |b MPQ |c 2003 | |
| 300 | |a 247 S. |b graph. Darst. : 30 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Zugl.: Innsbruck, Univ., Diss., 2003 | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010403435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010403435 | |
Record in the Search Index
| _version_ | 1807229061409275904 |
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| adam_text |
CONTENTS
I
BASIC
CONCEPTS
9
1
QUANTUM
STATES
13
1.1
PURE
STATES
.
13
1.1.1
SCHMIDT
DECOMPOSITION
.
14
1.1.2
ENTANGLEMENT
MEASURES
.
14
PROPERTIES
.
15
1.2
MIXED
STATES
.
17
1.2.1
THE
SEPARABILITY
PROBLEM
.
17
BIPARTITE
CASE
.
18
MULTIPARTITE
CASE
.
20
ENTANGLEMENT
WITNESSES
AND
POSITIVE
MAPS
.
22
1.2.2
THE
DISTILLATION
AND
ACTIVATION
PROBLEMS
.
26
1.3
GAUSSIAN
STATES
.
27
1.3.1
PURE
STATES
.
30
MEASURES
OF
ENTANGLEMENT
AND
SQUEEZING
.
31
1.3.2
MIXED
STATES
.
33
THE
SEPARABILITY
PROBLEM
.
33
2
QUANTUM
OPERATIONS
35
2.1
COMPLETELY
POSITIVE
MAPS
.
35
2.2
GAUSSIAN
OPERATORS
.
36
2.2.1
SYMPLECTIC
TRANSFORMATION
.
37
II
ENTANGLEMENT
PROPERTIES
OF
QUANTUM
OPERATIONS
39
3
INTRODUCTION
41
4
OPERATORS
ACTING
ON
A
FINITE
DIMENSIONAL
HILBERT
SPACE
42
4.1
CHARACTERIZATION
AND
IMPLEMENTATION
.
42
4.1.1
ISOMORPHISM
BETWEEN
COMPLETELY
POSITIVE
MAPS
AND
POSITIVE
SEMIDEFINITE
OPERATORS
.
44
4.1.2
CHARACTERIZATION
ACCORDING
TO
ENTANGLEMENT
PROPERTIES
45
4.1.3
ILLUSTRATIVE
EXAMPLES
.
46
4.1.4
IMPLEMENTATION
USING
A
SMALL
AMOUNT
OF
ENTANGLEMENT
48
4.1.5
GENERALIZATION
TO
MULTI-PARTITE
SYSTEMS
.
49
4.1.6
CONCLUSIONS
.
50
4.2
OPTIMAL
CREATION
OF
ENTANGLEMENT
USING
A
TWO-QUBIT
GATE
.
51
4.2.1
UNITARY
TWO-QUBIT
OPERATIONS
.
52
DECOMPOSITION
.
52
4.2.2
TWO
QUBITS
.
56
4.2.3
THE
ROLE
OF
AUXILIARY
SYSTEMS
.
58
DEPENDENCE
ON
THE
ENTANGLEMENT
MEASURE
.
59
EXAMPLES
.
60
4.2.4
CONCLUSIONS
.
62
5
OPERATORS
ACTING
ON
AN
INFINITE
DIMENSIONAL
HILBERT
SPACE
(GAUSSIAN
OPERATORS)
64
5.1
SIMULATION
OF
INTERACTIONS
.
66
5.1.1
HAMILTONIAN
SIMULATION
.
67
NECESSARY
AND
SUFFICIENT
CONDITION
.
67
DISCUSSION
.
69
APPLICATION
TO
X
L
X
2
-INTERACTION
.
70
5.1.2
GATE
SIMULATION
AND
STATE
ENGINEERING
.
71
5.2
CREATION
OF
ENTANGLEMENT
AND
SQUEEZING
.
72
5.2.1
OPTIMAL
ENTANGLEMENT/SQUEEZING
RATES
.
74
ENTANGLEMENT
RATE
.
74
SQUEEZING
RATE
.
78
5.2.2
OPTIMAL
ENTANGLEMENT
GENERATION
FROM
THE
VACUUM
STATE
80
5.3
DISCUSSION
AND
CONCLUSION
.
85
III
ENTANGLEMENT
PROPERTIES
OF
QUANTUM
STATES
87
6
INTRODUCTION
89
7
THE
SEPARABILITY
PROBLEM
91
7.1
FINITE
DIMENSIONAL
HILBERT
SPACE
.
92
7.1.1
C
2
C
N
COMPOSITE
QUANTUM
SYSTEMS
.
92
DEFINITIONS
AND
NOTATION
.
I
.
94
PRODUCT
VECTORS
.
95
6
RESULTS
.
104
EXAMPLE:
C
2
C
4
.
109
CONCLUSIONS
.
.
.
112
7.1.2
ENTANGLEMENT
WITNESSES
AND
BOUND
ENTANGLED
STATES
.
.
112
DEFINITIONS
AND
NOTATION
.
114
GENERAL
ENTANGLEMENT
WITNESSES
.
115
NON-DECOMPOSABLE
ENTANGLEMENT
WITNESSES
.
120
OPTIMIZATION
.
123
POSITIVE
MAPS
.
127
ILLUSTRATION
.
129
SUFFICIENT
CONDITION
FOR
INSEPARABILITY
.
135
CHARACTERIZATION
OF
ENTANGLEMENT
WITNESSES
AND
POSI
TIVE
MAPS
.
135
ENTANGLEMENT
WITNESSES
AND
EDGE
STATES
FOR
TV-PARTITE
SYSTEMS
.
138
CONCLUSIONS
.
140
7.1.3
SYMMETRIC
STATES
.
142
MIXED
STATES
.
144
PURE
STATES
.
146
7.1.4
THREE
QUBIT
STATES
.
148
EXAMPLES
OF
PPTES
.
149
7.2
INFINITE
DIMENSIONAL
HILBERT
SPACE
(CONTINUOUS
VARIABLE
SYSTEMS)
152
POSITIVITY
OF
SYMMETRIC
MATRICES
.
153
7.2.1
SEPARABILITY
CRITERION
FOR
BIPARTITE
GAUSSIAN
STATES
.
.
154
PHYSICAL
INTERPRETATION
.
159
7.2.2
THREE-MODE
GAUSSIAN
STATES
.
161
CLASSIFICATION
.
161
CRITERION
FOR
FULL
SEPARABILITY
.
163
EXAMPLES
OF
BOUND
ENTANGLED
STATES
.
169
CONCLUSIONS
.
174
8
THE
DISTILLATION
AND
ACTIVATION
PROBLEMS
176
8.1
NOTATION
AND
REVIEW
.
177
8.2
CHARACTERIZATION
USING
ENTANGLEMENT
WITNESSES
.
181
8.2.1
TWO
PARTIES
.
182
8.2.2
THREE
PARTIES
.
184
8.3
APPLICATIONS
.
187
8.3.1
TWO
PARTIES
.
188
8.3.2
EXAMPLE
OF
A
1-UNACTIVATABLE
THREE-PARTITE
STATE
.
.
.
188
8.4
CONCLUSIONS
.
189
7
9
CONCLUSIONS
190
10
NOTATION
AND
ABBREVIATIONS
193
11
LIST
OF
PUBLICATIONS
197
A
PROPERTIES
OF
MATRICES
201
B
TWO-QUBIT
GATES
203
B.L
PERIODICITY
AND
SYMMETRY
.
203
B.2
CREATION
OF
MAXIMALLY
ENTANGLED
STATES
.
204
B.3
BEST
INPUT
STATE
FOR
EXAMPLE
2
OF
SEC.
4.2.3
.
204
C
INTERACTION
SIMULATION
(INFINITE
DIMENSIONAL
HILBERT
SPACE)
206
C.L
HAMILTONIAN
SIMULATION
.
206
C.2
GATE
SIMULATION
.
208
D
SOLVING
POLYNOMIAL
EQUATIONS
210
D.L
REDUCTION
OF
ONE
POLYNOMIAL
.
210
D.2
REDUCTION
OF
TWO
POLYNOMIALS
.
211
E
OPTIMIZATION
OF
ENTANGLEMENT
WITNESSES
AND
PPTES
213
E.L
OPTIMALITY
OF
ENTANGLEMENT
WITNESSES
.
213
E.L.L
DEFINITIONS
AND
NOTATION
.
214
E.L.
2
DETERMINING
PW
.
215
E.1.3
NECESSARY
AND
SUFFICIENT
CONDITIONS
FOR
SUBTRACTING
AN
OPERATOR
.
216
E.L.
4
NECESSARY
AND
SUFFICIENT
CONDITIONS
FOR
^(W)
=
0
.
.
.
218
E.L.
5
OPTIMALITY
TEST
.
219
E.L.
6
NECESSARY
AND
SUFFICIENT
CONDITIONS
FOR
X(W)
=
0
.
.
.
219
E.2
EXAMPLE
OF
AN
OPTIMAL
ENTANGLEMENT
WITNESS
.
221
E.3
CANONICAL
FORM
OF
PPTES
.
222
F
INTERPRETATION
OF
SEPARABILITY
CRITERION
225
G
DETAILS
FOR
3-MODE
GAUSSIAN
STATES
228
G.L
POINTS
OF
INTERSECTION
.
228
G.2
CHARACTERIZATION
OF
K
.
229
H
DISTILLATION/ACTIVATION
IN
TERMS
OF
COMPLETELY
POSITIVE
MAPS
231
H.L
TWO
PARTIES
.
231
H.2
THREE
PARTIES
.
232
8 |
| any_adam_object | 1 |
| author | Kraus, Barbara 1975- |
| author_GND | (DE-588)1294886754 |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV017260796 |
| illustrated | Illustrated |
| indexdate | 2024-08-13T00:12:18Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010403435 |
| oclc_num | 76507522 |
| open_access_boolean | |
| owner | DE-12 DE-19 DE-BY-UBM |
| owner_facet | DE-12 DE-19 DE-BY-UBM |
| physical | 247 S. graph. Darst. : 30 cm |
| publishDate | 2003 |
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| spelling | Kraus, Barbara 1975- Verfasser (DE-588)1294886754 aut Entanglement properties of quantum states and quantum operations eingereicht von Barbara Kraus. [Max-Planck-Institut für Quantenoptik] Als Ms. des Autors gedr. Garching MPQ 2003 247 S. graph. Darst. : 30 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Innsbruck, Univ., Diss., 2003 (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010403435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kraus, Barbara 1975- Entanglement properties of quantum states and quantum operations |
| subject_GND | (DE-588)4113937-9 |
| title | Entanglement properties of quantum states and quantum operations |
| title_auth | Entanglement properties of quantum states and quantum operations |
| title_exact_search | Entanglement properties of quantum states and quantum operations |
| title_full | Entanglement properties of quantum states and quantum operations eingereicht von Barbara Kraus. [Max-Planck-Institut für Quantenoptik] |
| title_fullStr | Entanglement properties of quantum states and quantum operations eingereicht von Barbara Kraus. [Max-Planck-Institut für Quantenoptik] |
| title_full_unstemmed | Entanglement properties of quantum states and quantum operations eingereicht von Barbara Kraus. [Max-Planck-Institut für Quantenoptik] |
| title_short | Entanglement properties of quantum states and quantum operations |
| title_sort | entanglement properties of quantum states and quantum operations |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010403435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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