Dynamics, information and complexity in quantum systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Berlin]
Springer
2009
|
| Schriftenreihe: | Theoretical and mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Auch angekündigt als: Benatti, Fabio: Quantum entropies |
| Beschreibung: | XI, 535 S. |
| ISBN: | 9781402093050 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035401709 | ||
| 003 | DE-604 | ||
| 005 | 20090713 | ||
| 007 | t | ||
| 008 | 090331s2009 gw |||| 00||| eng d | ||
| 015 | |a 08,N39,0679 |2 dnb | ||
| 016 | 7 | |a 990359387 |2 DE-101 | |
| 020 | |a 9781402093050 |c Gb. : ca. EUR 96.25 (freier Pr.), ca. sfr 149.50 (freier Pr.) |9 978-1-4020-9305-0 | ||
| 024 | 3 | |a 9781402093050 | |
| 028 | 5 | 2 | |a 12271856 |
| 035 | |a (OCoLC)633492455 | ||
| 035 | |a (DE-599)DNB990359387 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-703 |a DE-29T |a DE-11 |a DE-19 | ||
| 084 | |a UK 1200 |0 (DE-625)145792: |2 rvk | ||
| 084 | |a 530 |2 sdnb | ||
| 100 | 1 | |a Benatti, Fabio |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamics, information and complexity in quantum systems |c Fabio Benatti |
| 246 | 1 | 3 | |a Quantum entropies |
| 264 | 1 | |a [Berlin] |b Springer |c 2009 | |
| 300 | |a XI, 535 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Theoretical and mathematical physics | |
| 500 | |a Auch angekündigt als: Benatti, Fabio: Quantum entropies | ||
| 650 | 0 | 7 | |a Dynamik |0 (DE-588)4013384-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexes System |0 (DE-588)4114261-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenmechanisches System |0 (DE-588)4300046-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenmechanisches System |0 (DE-588)4300046-0 |D s |
| 689 | 0 | 1 | |a Komplexes System |0 (DE-588)4114261-5 |D s |
| 689 | 0 | 2 | |a Dynamik |0 (DE-588)4013384-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4020-9306-7 |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017322343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017322343 | ||
Datensatz im Suchindex
| _version_ | 1804138829652688896 |
|---|---|
| adam_text | Titel: Dynamics, information and complexity in quantum systems
Autor: Benatti, Fabio
Jahr: 2009
Contents
Introduction
Part I Classical Dynamical Systems
Classical Dynamics and Ergodic Theory.................. 9
2.1 Classical Dynamical Systems............................. 10
2.1.1 Shift Dynamical Systems.......................... 20
2.2 Symbolic Dynamics..................................... 25
2.2.1 Algebraic Formulations............................ 29
2.2.2 Conditional Probabilities and Expectations.......... 34
2.2.3 Dynamical Shifts and Classical Spin Chains.......... 37
2.3 Ergodicity and Mixing.................................. 40
2.3.1 X-Systems...................................... 49
2.3.2 Ergodicity and Convexity ......................... 54
2.4 Information and Entropy................................ 56
2.4.1 Transmission Channels............................ 57
2.4.2 Stationary Information Sources .................... 59
2.4.3 Shannon Entropy................................. 61
2.4.4 Conditional Entropy.............................. 63
2.4.5 Mutual Information............................... 67
Dynamical Entropy and Information...................... 71
3.1 Dynamical Entropy..................................... 71
3.1.1 Entropic K-systems .............................. 80
3.2 Codes and Shannon Theorems ........................... 86
3.2.1 Source Compression.............................. 90
3.2.2 Channel Capacity................................ 98
Algorithmic Complexity.................................. 105
4.1 Effective Descriptions................................... 106
4.1.1 Classical Turing Machines......................... 108
4.1.2 Kolmogorov Complexity........................... 113
4.2 Algorithmic Complexity and Entropy Rate ................ 122
4.3 Prefix Algorithmic Complexity........................... 127
IX
X Contents
Part II Quantum Dynamical Systems
Quantum Mechanics of Finite Degrees of Freedom........139
5.1 Hilbert Space and Operator Algebras .....................139
5.2 C* Algebras...........................................143
5.2.1 Positive Operators................................148
5.2.2 Positive and Completely Positive Maps..............157
5.3 von Neumann Algebras..................................166
5.3.1 States and GNS Representation....................170
5.3.2 C* and von Neumann Abelian algebras .............173
5.4 Quantum Systems with Finite Degrees of Freedom..........178
5.5 Quantum States........................................190
5.5.1 States in the Algebraic Approach...................208
5.5.2 Density Matrices and von Neumann Entropy.........213
5.5.3 Composite Systems...............................218
5.5.4 Entangled States.................................222
5.6 Dynamics and State-Transformations .....................227
5.6.1 Quantum Operations.............................236
5.6.2 Open Quantum Dynamics.........................241
5.6.3 Quantum Dynamical Semigroups...................247
5.6.4 Physical Operations and Positive Maps..............251
Quantum Information Theory ............................255
6.1 Quantum Information Theory............................255
6.2 Bipartite Entanglement .................................261
6.3 Relative Entropy.......................................287
6.3.1 Holevo s Bound and the Entropy of a Subalgebra.....294
6.3.2 Entropy of a Subalgebra and Entanglement of
Formation.......................................302
Quantum Mechanics of Infinite Degrees of Freedom ......317
7.1 Observables, States and Dynamics........................323
7.1.1 Bosons and Fermions.............................325
7.1.2 GNS Representation and Dynamics.................335
7.1.3 Quantum Ergodicity and Mixing...................341
7.1.4 Algebraic Quantum K-Systems ....................356
7.1.5 Quantum Spin Chains ............................362
7.2 von Neumann Entropy Rate.............................376
7.3 Quantum Spin Chains as Quantum Sources................381
7.3.1 Quantum Compression Theorems...................383
7.3.2 Quantum Capacities..............................399
Contents XI
Part III Quantum Dynamical Entropies and Complexities
8 Quantum Dynamical Entropies...........................411
8.1 CNT Entropy: Decompositions of States ..................413
8.1.1 CNT Entropy: Quasi-Local Algebras................429
8.1.2 CNT Entropy: Stationary Couplings................433
8.1.3 CNT entropy: Applications........................436
8.1.4 Entropic Quantum /{ -systems .....................443
8.2 AFL Entropy: OPUs....................................451
8.2.1 Quantum Symbolic Models and AFL Entropy........452
8.2.2 AFL Entropy: Interpretation.......................455
8.2.3 ^IFi^Entropy: Applications........................457
8.2.4 AFL Entropy and Quantum Channel Capacities......475
9 Quantum Algorithmic Complexities ......................483
9.1 Effective Quantum Descriptions..........................484
9.1.1 Effective Descriptions by qubit Strings..............485
9.1.2 Quantum Turing Machines........................486
9.2 qubit Quantum Complexity..............................494
9.2.1 Quantum Brudno s Theorem.......................497
9.3 chit Quantum Complexity...............................506
References....................................................517
Index.........................................................527
|
| any_adam_object | 1 |
| author | Benatti, Fabio |
| author_facet | Benatti, Fabio |
| author_role | aut |
| author_sort | Benatti, Fabio |
| author_variant | f b fb |
| building | Verbundindex |
| bvnumber | BV035401709 |
| classification_rvk | UK 1200 |
| ctrlnum | (OCoLC)633492455 (DE-599)DNB990359387 |
| discipline | Physik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01883nam a2200481 c 4500</leader><controlfield tag="001">BV035401709</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090713 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090331s2009 gw |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">08,N39,0679</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">990359387</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781402093050</subfield><subfield code="c">Gb. : ca. EUR 96.25 (freier Pr.), ca. sfr 149.50 (freier Pr.)</subfield><subfield code="9">978-1-4020-9305-0</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9781402093050</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">12271856</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)633492455</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB990359387</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UK 1200</subfield><subfield code="0">(DE-625)145792:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">530</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Benatti, Fabio</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dynamics, information and complexity in quantum systems</subfield><subfield code="c">Fabio Benatti</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Quantum entropies</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">[Berlin]</subfield><subfield code="b">Springer</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 535 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Theoretical and mathematical physics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Auch angekündigt als: Benatti, Fabio: Quantum entropies</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dynamik</subfield><subfield code="0">(DE-588)4013384-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexes System</subfield><subfield code="0">(DE-588)4114261-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantenmechanisches System</subfield><subfield code="0">(DE-588)4300046-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Quantenmechanisches System</subfield><subfield code="0">(DE-588)4300046-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Komplexes System</subfield><subfield code="0">(DE-588)4114261-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Dynamik</subfield><subfield code="0">(DE-588)4013384-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4020-9306-7</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017322343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017322343</subfield></datafield></record></collection> |
| id | DE-604.BV035401709 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:34:25Z |
| institution | BVB |
| isbn | 9781402093050 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017322343 |
| oclc_num | 633492455 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-29T DE-11 DE-19 DE-BY-UBM |
| physical | XI, 535 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Theoretical and mathematical physics |
| spelling | Benatti, Fabio Verfasser aut Dynamics, information and complexity in quantum systems Fabio Benatti Quantum entropies [Berlin] Springer 2009 XI, 535 S. txt rdacontent n rdamedia nc rdacarrier Theoretical and mathematical physics Auch angekündigt als: Benatti, Fabio: Quantum entropies Dynamik (DE-588)4013384-9 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 s Komplexes System (DE-588)4114261-5 s Dynamik (DE-588)4013384-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4020-9306-7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017322343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benatti, Fabio Dynamics, information and complexity in quantum systems Dynamik (DE-588)4013384-9 gnd Komplexes System (DE-588)4114261-5 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| subject_GND | (DE-588)4013384-9 (DE-588)4114261-5 (DE-588)4300046-0 |
| title | Dynamics, information and complexity in quantum systems |
| title_alt | Quantum entropies |
| title_auth | Dynamics, information and complexity in quantum systems |
| title_exact_search | Dynamics, information and complexity in quantum systems |
| title_full | Dynamics, information and complexity in quantum systems Fabio Benatti |
| title_fullStr | Dynamics, information and complexity in quantum systems Fabio Benatti |
| title_full_unstemmed | Dynamics, information and complexity in quantum systems Fabio Benatti |
| title_short | Dynamics, information and complexity in quantum systems |
| title_sort | dynamics information and complexity in quantum systems |
| topic | Dynamik (DE-588)4013384-9 gnd Komplexes System (DE-588)4114261-5 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| topic_facet | Dynamik Komplexes System Quantenmechanisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017322343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT benattifabio dynamicsinformationandcomplexityinquantumsystems AT benattifabio quantumentropies |