Principles of quantum computation and information: 2 Basic tools and special topics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2007
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII S., S. 257 - 680 Ill., graph. Darst. |
| ISBN: | 9789812563453 9789812565280 9812563458 9812565280 |
Internformat
MARC
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|---|---|---|---|
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| 007 | t | ||
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| 020 | |a 9789812563453 |9 978-981-256-345-3 | ||
| 020 | |a 9789812565280 |9 978-981-256-528-0 | ||
| 020 | |a 9812563458 |9 981-256-345-8 | ||
| 020 | |a 9812565280 |9 981-256-528-0 | ||
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| 100 | 1 | |a Benenti, Giuliano |d 1969- |e Verfasser |0 (DE-588)131799592 |4 aut | |
| 245 | 1 | 0 | |a Principles of quantum computation and information |n 2 |p Basic tools and special topics |c Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2007 | |
| 300 | |a XVIII S., S. 257 - 680 |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Casati, Giulio |d 1942- |e Sonstige |0 (DE-588)131799630 |4 oth | |
| 700 | 1 | |a Strini, Giuliano |d 1937- |e Sonstige |0 (DE-588)131799665 |4 oth | |
| 773 | 0 | 8 | |w (DE-604)BV019351405 |g 2 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-013139086 | ||
Datensatz im Suchindex
| _version_ | 1804133313213890560 |
|---|---|
| adam_text | Contents - Volume
II
Preface vii
5. Quantum Information
Theory
257
5.1
The density matrix
....................... 258
5.1.1
The density matrix for a qubit
............ 264
5.1.2
Composite systems
................... 267
5.1.3 *
The quantum copying machine
........... 271
5.2
The Schmidt decomposition
.................. 273
5.3
Purification
........................... 276
5.4
The
Kraus
representation
................... 278
5.5
Measurement of the density matrix for a qubit
....... 284
5.6
Generalized measurements
................... 286
5.6.1 *
Weak measurements
................. 288
5.6.2
POVM measurements
................. 290
5.7
The Shannon entropy
..................... 293
5.8
Classical data compression
................... 294
5.8.1
Shannon s noiseless coding theorem
.......... 294
5.8.2
Examples of data compression
............. 296
5.9
The
von
Neumann entropy
.................. 297
5.9.1
Example
1:
source of orthogonal pure states
..... 299
5.9.2
Example
2:
source of non-orthogonal pure states
. . 300
5.10
Quantum data compression
.................. 303
5.10.1
Schumacher s quantum noiseless coding theorem
. . . 303
5.10.2
Compression of an n-qubit message
.......... 304
5.10.3
Example
1:
two-qubit messages
............ 306
5.10.4
Example
2:
three-qubit messages
........... 308
xvi
Principles of Quantum Computation and Information. II
5.11
Accessible information
..................... 311
5.11.1
The Holevo bound
................... 313
5.11.2
Example
1:
two non-orthogonal pure states
..... 313
5.11.3 *
Example
2:
three non-orthogonal pure states
. . . 317
5.12
Entanglement concentration and
von
Neumann entropy
. . 319
5.13
The Peres separability criterion
................ 323
5.14*
Entropies in physics
..................... 325
5.14.1 *
Thermodynamic entropy
............... 325
5.14.2 *
Statistical entropy
.................. 328
5.14.3 *
Dynamical Kolmogorov-Sinai entropy
....... 330
5.15
A guide to the bibliography
.................. 333
6.
Decoherence
335
6.1
Decoherence models for a single qubit
............ 336
6.1.1
The quantum black box
................ 337
6.1.2
Measuring a quantum operation acting on a qubit
. . 339
6.1.3
Quantum circuits simulating noise channels
..... 340
6.1.4
The bit-flip channel
................... 343
6.1.5
The phase-flip channel
................. 344
6.1.6
The bit-phase-flip channel
............... 345
6.1.7
The depolarizing channel
................ 346
6.1.8
Amplitude damping
................... 347
6.1.9
Phase damping
..................... 349
6.1.10
De-entanglement
.................... 351
6.2
The master equation
...................... 354
6.2.1 *
Derivation of the master equation
.......... 355
6.2.2 *
The master equation and quantum operations
. . . 359
6.2.3
The master equation for a single qubit
........ 362
6.3
Quantum to classical transition
................ 365
6.3.1 Schrödinger s
cat
.................... 365
6.3.2
Decoherence and destruction of cat states
...... 367
6.4 *
Decoherence and quantum measurements
......... 375
6.5 *
Quantum chaos
........................ 378
6.5.1 *
Dynamical chaos in classical mechanics
....... 379
6.5.2 *
Quantum chaos and the correspondence principle
. 382
6.5.3 *
Time scales of quantum chaos
............ 385
6.5.4 *
Quantum chaos and Anderson localization
..... 392
6.5.5 *
The hydrogen atom in a microwave field
...... 395
6.5.6 *
Quantum chaos and universal spectral fluctuations
400
Contents - Volume
II
xvii
6.5.7 * The
chaos border
for the quantum computer hardware
412
6.5.8 *
The quantum Loschmidt echo
............ 416
6.5.9 *
Dynamical stability of quantum motion
...... 423
6.5.10 *
Dynamical chaos and dephasing: the double-slit ex¬
periment
......................... 425
6.5.11 *
Entanglement and chaos
............... 430
6.6
Decoherence and quantum computation
........... 434
6.6.1 *
Decoherence and quantum trajectories
....... 439
6.7 *
Quantum computation and quantum chaos
........ 449
6.7.1 *
Quantum versus classical errors
........... 451
6.7.2 *
Static imperfections versus noisy gates
....... 452
6.8
A guide to the bibliography
.................. 457
7.
Quantum Error Correction
459
7.1
The three-qubit bit-flip code
.................. 461
7.2
The three-qubit phase-flip code
................ 465
7.3
The nine-qubit Shor code
................... 466
7.4
General properties of quantum error correction
....... 471
7.4.1
The quantum Hamming bound
............ 473
7.5 *
The five-qubit code
...................... 474
7.6 *
Classical linear codes
..................... 476
7.6.1 *
The Hamming codes
................. 478
7.7 *
CSS codes
........................... 481
7.8
Decoherence-free subspaces
.................. 484
7.8.1 *
Conditions for decoherence-free dynamics
..... 486
7.8.2 *
The spin-boson model
................ 488
7.9 *
The
Zeno
effect
........................ 490
7.10
Fault-tolerant quantum computation
............. 494
7.10.1
Avoidance of error propagation
............ 495
7.10.2
Fault-tolerant quantum gates
............. 497
7.10.3
The noise threshold for quantum computation
.... 497
7.11 *
Quantum cryptography over noisy channels
........ 500
7.12*
Quantum channels with memory
.............. 506
7.13
A guide to the bibliography
.................. 510
8.
First Experimental Implementations
513
8.1
NMR quantum computation
.................. 514
8.1.1
The system Hamiltonian
................ 515
xviii
Principles of Quantum Computation and Information. II
8.1.2
The physical apparatus
................. 518
8.1.3
Quantum ensemble computation
........... 519
8.1.4
Refocusing
........................ 522
8.1.5
Demonstration of quantum algorithms
........ 523
8.2
Cavity quantum electrodynamics
............... 528
8.2.1
Rabi
oscillations
..................... 535
8.2.2
Entanglement generation
................ 538
8.2.3
The quantum phase gate
................ 542
8.3
The ion-trap quantum computer
............... 544
8.3.1
The Paul trap
...................... 544
8.3.2
Laser pulses
....................... 547
8.3.3
Realization of the Cirac-Zoller
CNOT
gate
..... 554
8.3.4
Entanglement generation
................ 556
8.4
Solid state qubits
........................ 561
8.4.1
Spins in semiconductors
................ 561
8.4.2
Quantum dots
...................... 562
8.4.3
Superconducting qubit circuits
............ 566
8.5
Quantum communication with photons
............ 573
8.5.1
Linear optics
...................... 573
8.5.2
Experimental quantum
teleportation
......... 578
8.5.3
Experimental quantum-key distribution
....... 587
8.6
Problems and prospects
.................... 591
8.7
A guide to the bibliography
.................. 592
Appendix
В
Solutions to the exercises
595
Bibliography
657
Index
675
|
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| id | DE-604.BV019813705 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:06:44Z |
| institution | BVB |
| isbn | 9789812563453 9789812565280 9812563458 9812565280 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013139086 |
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| physical | XVIII S., S. 257 - 680 Ill., graph. Darst. |
| publishDate | 2007 |
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| publisher | World Scientific |
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| spelling | Benenti, Giuliano 1969- Verfasser (DE-588)131799592 aut Principles of quantum computation and information 2 Basic tools and special topics Giuliano Benenti and Giulio Casati ; Giuliano Strini New Jersey [u.a.] World Scientific 2007 XVIII S., S. 257 - 680 Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Casati, Giulio 1942- Sonstige (DE-588)131799630 oth Strini, Giuliano 1937- Sonstige (DE-588)131799665 oth (DE-604)BV019351405 2 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013139086&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benenti, Giuliano 1969- Principles of quantum computation and information |
| title | Principles of quantum computation and information |
| title_auth | Principles of quantum computation and information |
| title_exact_search | Principles of quantum computation and information |
| title_full | Principles of quantum computation and information 2 Basic tools and special topics Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| title_fullStr | Principles of quantum computation and information 2 Basic tools and special topics Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| title_full_unstemmed | Principles of quantum computation and information 2 Basic tools and special topics Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| title_short | Principles of quantum computation and information |
| title_sort | principles of quantum computation and information basic tools and special topics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013139086&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019351405 |
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