Atjaunināt sīkdatņu piekrišanu

E-grāmata: Quantum Information Theory: Mathematical Foundation

3.00/5 (2 ratings by Goodreads)
  • Formāts: PDF+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 03-Nov-2016
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783662497258
Citas grāmatas par šo tēmu:
  • Formāts - PDF+DRM
  • Cena: 88,63 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
Quantum Information Theory: Mathematical FoundationPalielināt
  • Formāts: PDF+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 03-Nov-2016
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783662497258
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides  lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption.
Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation.
With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained.
Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information.
To aid in understanding, each chapter is accompanied by a set of exercises and solutions.

1 Mathematical Formulation of Quantum Systems
1(24)
1.1 Quantum Systems and Linear Algebra
1(4)
1.2 State and Measurement in Quantum Systems
5(3)
1.3 Quantum Two-Level Systems
8(2)
1.4 Composite Systems and Tensor Products
10(5)
1.5 Matrix Inequalities and Matrix Monotone Functions
15(3)
1.6 Solutions of Exercises
18(7)
References
24(1)
2 Information Quantities and Parameter Estimation in Classical Systems
25(70)
2.1 Information Quantities in Classical Systems
25(20)
2.1.1 Entropy
25(2)
2.1.2 Relative Entropy
27(6)
2.1.3 Mutual Information
33(3)
2.1.4 The Independent and Identical Condition and Renyi Entropy
36(5)
2.1.5 Conditional Renyi Entropy
41(4)
2.2 Geometry of Probability Distribution Family
45(11)
2.2.1 Inner Product for Random Variables and Fisher Information
45(5)
2.2.2 Bregman Divergence
50(3)
2.2.3 Exponential Family and Divergence
53(3)
2.3 Estimation in Classical Systems
56(5)
2.4 Type Method and Large Deviation Evaluation
61(10)
2.4.1 Type Method and Sanov's Theorem
61(3)
2.4.2 Cramer Theorem and Its Application to Estimation
64(7)
2.5 Continuity and Axiomatic Approach
71(6)
2.6 Large Deviation on Sphere
77(7)
2.7 Related Books
84(1)
2.8 Solutions of Exercises
84(11)
References
93(2)
3 Quantum Hypothesis Testing and Discrimination of Quantum States
95(60)
3.1 Information Quantities in Quantum Systems
95(10)
3.1.1 Quantum Entropic Information Quantities
95(6)
3.1.2 Other Quantum Information Quantities
101(4)
3.2 Two-State Discrimination in Quantum Systems
105(5)
3.3 Discrimination of Plural Quantum States
110(2)
3.4 Asymptotic Analysis of State Discrimination
112(3)
3.5 Hypothesis Testing and Stein's Lemma
115(6)
3.6 Hypothesis Testing by Separable Measurements
121(2)
3.7 Proof of Direct Part of Stein's Lemma and Hoeffding Bound
123(4)
3.8 Information Inequalities and Proof of Converse Part of Stein's Lemma and Han-Kobayashi Bound
127(10)
3.9 Proof of Theorem 3.1
137(1)
3.10 Historical Note
138(2)
3.11 Solutions of Exercises
140(15)
References
151(4)
4 Classical-Quantum Channel Coding (Message Transmission)
155(42)
4.1 Formulation of the Channel Coding Process in Quantum Systems
156(6)
4.1.1 Transmission Information in C-Q Channels and Its Properties
157(1)
4.1.2 C-Q Channel Coding Theorem
158(4)
4.2 Coding Protocols with Adaptive Decoding and Feedback
162(2)
4.3 Channel Capacities Under Cost Constraint
164(2)
4.4 A Fundamental Lemma
166(1)
4.5 Proof of Direct Part of C-Q Channel Coding Theorem
167(4)
4.6 Proof of Converse Part of C-Q Channel Coding Theorem
171(7)
4.7 Pseudoclassical Channels
178(2)
4.8 Historical Note
180(2)
4.8.1 C-Q Channel Capacity
180(1)
4.8.2 Hypothesis Testing Approach
181(1)
4.8.3 Other Topics
182(1)
4.9 Solutions of Exercises
182(15)
References
193(4)
5 State Evolution and Trace-Preserving Completely Positive Maps
197(56)
5.1 Description of State Evolution in Quantum Systems
197(8)
5.2 Examples of Trace-Preserving Completely Positive Maps
205(6)
5.3 State Evolutions in Quantum Two-Level Systems
211(5)
5.4 Information-Processing Inequalities in Quantum Systems
216(5)
5.5 Entropy Inequalities in Quantum Systems
221(7)
5.6 Conditional Renyi Entropy and Duality
228(6)
5.7 Proof and Construction of Stinespring and Choi-Kraus Representations
234(4)
5.8 Historical Note
238(1)
5.8.1 Completely Positive Map and Quantum Relative Entropy
238(1)
5.8.2 Quantum Relative Renyi entropy
239(1)
5.9 Solutions of Exercises
239(14)
References
250(3)
6 Quantum Information Geometry and Quantum Estimation
253(70)
6.1 Inner Products in Quantum Systems
253(6)
6.2 Metric-Induced Inner Products
259(6)
6.3 Geodesies and Divergences
265(8)
6.4 Quantum State Estimation
273(5)
6.5 Large Deviation Evaluation
278(3)
6.6 Multiparameter Estimation
281(9)
6.7 Relative Modular Operator and Quantum f-Relative Entropy
290(10)
6.7.1 Monotonicity Under Completely Positivity
290(3)
6.7.2 Monotonicity Under 2-Positivity
293(7)
6.8 Historical Note
300(4)
6.8.1 Quantum State Estimation
300(1)
6.8.2 Quantum Channel Estimation
301(1)
6.8.3 Geometry of Quantum States
302(1)
6.8.4 Equality Condition for Monotonicity of Relative Entropy
303(1)
6.9 Solutions of Exercises
304(19)
References
318(5)
7 Quantum Measurements and State Reduction
323(34)
7.1 State Reduction Due to Quantum Measurement
323(6)
7.2 Uncertainty and Measurement
329(10)
7.2.1 Uncertainties for Observable and Measurement
329(2)
7.2.2 Disturbance
331(1)
7.2.3 Uncertainty Relations
332(7)
7.3 Entropic Uncertainty Relation
339(3)
7.4 Measurements with Negligible State Reduction
342(4)
7.5 Historical Note
346(2)
7.6 Solutions of Exercises
348(9)
References
355(2)
8 Entanglement and Locality Restrictions
357(134)
8.1 Entanglement and Local Quantum Operations
357(5)
8.2 Fidelity and Entanglement
362(7)
8.3 Entanglement and Information Quantities
369(6)
8.4 Entanglement and Majorization
375(5)
8.5 Distillation of Maximally Entangled States
380(7)
8.6 Dilution of Maximally Entangled States
387(4)
8.7 Unified Approach to Distillation and Dilution
391(7)
8.8 Maximally Correlated State
398(5)
8.9 Dilution with Zero-Rate Communication
403(3)
8.10 Discord
406(6)
8.11 State Generation from Shared Randomness
412(6)
8.12 Positive Partial Transpose (PPT) Operations
418(8)
8.13 Violation of Superadditivity of Entanglement Formation
426(7)
8.13.1 Counter Example for Superadditivity of Entanglement Formation
426(2)
8.13.2 Proof of Theorem 8.14
428(5)
8.14 Secure Random Number Generation
433(5)
8.14.1 Security Criteria and Their Evaluation
433(3)
8.14.2 Proof of Theorem 8.15
436(2)
8.15 Duality Between Two Conditional Entropies
438(5)
8.15.1 Recovery of Maximally Entangled State from Evaluation of Classical Information
438(4)
8.15.2 Duality Between Two Conditional Entropies of Mutually Unbiased Basis
442(1)
8.16 Examples
443(7)
8.16.1 2 × 2 System
444(1)
8.16.2 Werner State
445(2)
8.16.3 Isotropic State
447(3)
8.17 Proof of Theorem 8.2
450(4)
8.18 Proof of Theorem 8.3
454(1)
8.19 Proof of Theorem 8.8 for Mixed States
455(1)
8.20 Proof of Theorem 8.9 for Mixed States
456(3)
8.20.1 Proof of Direct Part
456(1)
8.20.2 Proof of Converse Part
457(2)
8.21 Historical Note
459(2)
8.21.1 Entanglement Distillation
459(1)
8.21.2 Entanglement Dilution and Related Topics
460(1)
8.21.3 Additivity
460(1)
8.21.4 Security and Related Topics
461(1)
8.22 Solutions of Exercises
461(30)
References
486(5)
9 Analysis of Quantum Communication Protocols
491(78)
9.1 Quantum Teleportation
491(2)
9.2 C-Q Channel Coding with Entangled Inputs
493(8)
9.3 C-Q Channel Coding with Shared Entanglement
501(9)
9.4 Quantum Channel Resolvability
510(6)
9.5 Quantum-Channel Communications with an Eavesdropper
516(11)
9.5.1 C-Q Wiretap Channel
516(2)
9.5.2 Relation to BB84 Protocol
518(2)
9.5.3 Secret Sharing
520(1)
9.5.4 Distillation of Classical Secret Key
521(2)
9.5.5 Proof of Direct Part of C-Q Wiretap Channel Coding Theorem
523(2)
9.5.6 Proof of Converse Part of C-Q Wiretap Channel Coding Theorem
525(2)
9.6 Channel Capacity for Quantum-State Transmission
527(14)
9.6.1 Conventional Formulation
527(7)
9.6.2 Proof of Hashing Inequality (8.121)
534(1)
9.6.3 Decoder with Assistance by Local Operations
534(7)
9.7 Examples
541(7)
9.7.1 Group Covariance Formulas
541(2)
9.7.2 d-Dimensional Depolarizing Channel
543(1)
9.7.3 Transpose Depolarizing Channel
544(1)
9.7.4 Generalized Pauli Channel
545(1)
9.7.5 PNS Channel
545(1)
9.7.6 Erasure Channel
546(1)
9.7.7 Phase-Damping Channel
547(1)
9.8 Proof of Theorem 9.3
548(4)
9.9 Historical Note
552(3)
9.9.1 Additivity Conjecture
552(1)
9.9.2 Channel Coding with Shared Entanglement
553(1)
9.9.3 Quantum-State Transmission
554(1)
9.10 Solutions of Exercises
555(14)
References
565(4)
10 Source Coding in Quantum Systems
569(38)
10.1 Four Kinds of Source Coding Schemes in Quantum Systems
570(1)
10.2 Quantum Fixed-Length Source Coding
571(3)
10.3 Construction of a Quantum Fixed-Length Source Code
574(3)
10.4 Universal Quantum Fixed-Length Source Codes
577(2)
10.5 Universal Quantum Variable-Length Source Codes
579(1)
10.6 Mixed-State Case and Bipartite State Generation
580(6)
10.7 Compression with Classical Memory
586(4)
10.8 Compression with Shared Randomness
590(4)
10.9 Relation to Channel Capacities
594(3)
10.10 Proof of Lemma 10.3
597(2)
10.11 Historical Note
599(2)
10.12 Solutions of Exercises
601(6)
References
603(4)
Appendix: Limits and Linear Algebra 607(20)
Postface to Japanese version 627(4)
Index 631
Masahito Hayashi was born in Japan in 1971. He received the B.S. degree from the Faculty of Sciences in Kyoto University, Japan, in 1994 and the M.S. and Ph.D. degrees in Mathematics from Kyoto University, Japan, in 1996 and 1999, respectively.

He worked in Kyoto University as a Research Fellow of the Japan Society of the Promotion of Science (JSPS) from 1998 to 2000, and worked in the Laboratory for Mathematical Neuroscience, Brain Science Institute, RIKEN from 2000 to 2003, and worked in ERATO Quantum Computation and Information Project, Japan Science and Technology Agency (JST) as the Research Head from 2000 to 2006. He also worked in the Superrobust Computation Project Information Science and Technology Strategic Core (21st Century COE by MEXT) Graduate School of Information Science and Technology, The University of Tokyo as Adjunct Associate Professor from 2004 to 2007. He worked in the Graduate School of Information Sciences, Tohoku University as Associate Professor from2007 to 2012. In 2012, he joined the Graduate School of Mathematics, Nagoya University as Professor. He also worked in Centre for Quantum Technologies, National University of Singapore as Visiting Research Associate Professor from 2009 to 2012 and as Visiting Research Professor from 2012 to now. In 2011, he received the Information Theory Society Paper Award (2011) for Information-Spectrum Approach to Second-Order Coding Rate in Channel Coding. In 2016, he received the Japan Academy Medal from the Japan Academy and the JSPS Prize from Japan Society for the Promotion of Science.







He is a member of the Editorial Board of the International Journal of Quantum Information and International Journal On Advances in Security. His research interests include classical and quantum information theory, information-theoretic security, and classical and quantum statistical inference.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97836624972582e.html
Keywords: