國立虎尾科技大學 |

Quantum Information Processing with Finite Resources = Mathematical Foundations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Quantum Information Processing with Finite Resources/ by Marco Tomamichel.
其他題名:	Mathematical Foundations /
作者:	Tomamichel, Marco.
面頁冊數:	IX, 138 p. 4 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Quantum physics. -
電子資源:	https://doi.org/10.1007/978-3-319-21891-5
ISBN:	9783319218915

Quantum Information Processing with Finite Resources = Mathematical Foundations /
Tomamichel, Marco.

Quantum Information Processing with Finite ResourcesMathematical Foundations /[electronic resource] :by Marco Tomamichel. - 1st ed. 2016. - IX, 138 p. 4 illus. in color.online resource. - SpringerBriefs in Mathematical Physics,52197-1757 ;. - SpringerBriefs in Mathematical Physics,8.

Introduction -- Finite Resource Information Theory 1.2 Motivating Example -- Outline of the Book -- Modeling Quantum Information -- General Remarks on Notation -- Linear Operators and Events -- Functionals and States -- Multi-Partite Systems -- Functions on Positive Operators -- Quantum Channels -- Background and Further Reading -- Norms and Metrics -- Norms for Operators and Quantum States -- Trace Distance -- Fidelity -- Purified Distance -- Background and Further Reading -- Quantum Rényi Divergence -- Classical Rényi Divergence -- Classifying Quantum Rényi Divergences -- Minimal Quantum Rényi Divergence -- Petz Quantum Rényi Divergence -- Background and Further Reading -- Conditional Rényi Entropy -- Conditional Entropy from Divergence -- Definitions and Properties.-Duality Relations and their Applications -- Chain Rules -- Background and Further Reading -- Smooth Entropy Calculus -- Min- and Max-Entropy -- Smooth Entropies -- Properties of the Smooth Entropies -- Fully Quantum Asymptotic Equipartition Property -- Background and Further Reading -- Selected Applications -- Binary Quantum Hypothesis Testing -- Entropic Uncertainty Relations -- Randomness Extraction -- Background and Further Reading -- A Some Fundamental Matrix Analysis Results -- References.

This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigation possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.

ISBN: 9783319218915

Standard No.: 10.1007/978-3-319-21891-5doiSubjects--Topical Terms:

1179090
Quantum physics.

LC Class. No.: QC173.96-174.52

Dewey Class. No.: 530.12

Quantum Information Processing with Finite Resources = Mathematical Foundations /
LDR:03957nam a22003975i 4500 001 970909
003 DE-He213
005 20200630183141.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319218915 $9 978-3-319-21891-5
024 7 $a 10.1007/978-3-319-21891-5 $2 doi
035 $a 978-3-319-21891-5
050 4 $a QC173.96-174.52
072 7 $a PHQ $2 bicssc
072 7 $a SCI057000 $2 bisacsh
072 7 $a PHQ $2 thema
082 0 4 $a 530.12 $2 23
100 1 $a Tomamichel, Marco. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1103363
245 1 0 $a Quantum Information Processing with Finite Resources $h [electronic resource] : $b Mathematical Foundations / $c by Marco Tomamichel.
250 $a 1st ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a IX, 138 p. 4 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Mathematical Physics, $x 2197-1757 ; $v 5
505 0 $a Introduction -- Finite Resource Information Theory 1.2 Motivating Example -- Outline of the Book -- Modeling Quantum Information -- General Remarks on Notation -- Linear Operators and Events -- Functionals and States -- Multi-Partite Systems -- Functions on Positive Operators -- Quantum Channels -- Background and Further Reading -- Norms and Metrics -- Norms for Operators and Quantum States -- Trace Distance -- Fidelity -- Purified Distance -- Background and Further Reading -- Quantum Rényi Divergence -- Classical Rényi Divergence -- Classifying Quantum Rényi Divergences -- Minimal Quantum Rényi Divergence -- Petz Quantum Rényi Divergence -- Background and Further Reading -- Conditional Rényi Entropy -- Conditional Entropy from Divergence -- Definitions and Properties.-Duality Relations and their Applications -- Chain Rules -- Background and Further Reading -- Smooth Entropy Calculus -- Min- and Max-Entropy -- Smooth Entropies -- Properties of the Smooth Entropies -- Fully Quantum Asymptotic Equipartition Property -- Background and Further Reading -- Selected Applications -- Binary Quantum Hypothesis Testing -- Entropic Uncertainty Relations -- Randomness Extraction -- Background and Further Reading -- A Some Fundamental Matrix Analysis Results -- References.
520 $a This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigation possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.
650 0 $a Quantum physics. $3 1179090
650 0 $a Quantum computers. $3 564139
650 0 $a Data structures (Computer science). $3 680370
650 0 $a Spintronics. $3 580491
650 1 4 $a Quantum Physics. $3 671960
650 2 4 $a Quantum Computing. $3 883739
650 2 4 $a Data Structures and Information Theory. $3 1211601
650 2 4 $a Quantum Information Technology, Spintronics. $3 783474
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319218908
776 0 8 $i Printed edition: $z 9783319218922
830 0 $a SpringerBriefs in Mathematical Physics, $x 2197-1757 ; $v 8 $3 1263793
856 4 0 $u https://doi.org/10.1007/978-3-319-21891-5
912 $a ZDB-2-PHA
912 $a ZDB-2-SXP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Physics and Astronomy (R0) (SpringerNature-43715)