LEADER 05187nam 22007095 450 001 9910254611203321 005 20200630183141.0 010 $a3-319-21891-3 024 7 $a10.1007/978-3-319-21891-5 035 $a(CKB)3710000000492431 035 $a(EBL)4178443 035 $a(SSID)ssj0001585480 035 $a(PQKBManifestationID)16263367 035 $a(PQKBTitleCode)TC0001585480 035 $a(PQKBWorkID)14865742 035 $a(PQKB)11769272 035 $a(DE-He213)978-3-319-21891-5 035 $a(MiAaPQ)EBC4178443 035 $a(PPN)190526602 035 $a(EXLCZ)993710000000492431 100 $a20151014d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aQuantum Information Processing with Finite Resources $eMathematical Foundations /$fby Marco Tomamichel 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (146 p.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v5 300 $aDescription based upon print version of record. 311 $a3-319-21890-5 320 $aIncludes bibliographical references. 327 $aIntroduction -- 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. 330 $aThis book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigation possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v5 606 $aQuantum physics 606 $aQuantum computers 606 $aData structures (Computer science) 606 $aSpintronics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aQuantum Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/M14070 606 $aData Structures and Information Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/I15009 606 $aQuantum Information Technology, Spintronics$3https://scigraph.springernature.com/ontologies/product-market-codes/P31070 615 0$aQuantum physics. 615 0$aQuantum computers. 615 0$aData structures (Computer science). 615 0$aSpintronics. 615 14$aQuantum Physics. 615 24$aQuantum Computing. 615 24$aData Structures and Information Theory. 615 24$aQuantum Information Technology, Spintronics. 676 $a530 700 $aTomamichel$b Marco$4aut$4http://id.loc.gov/vocabulary/relators/aut$0810010 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254611203321 996 $aQuantum Information Processing with Finite Resources$92523459 997 $aUNINA