LEADER 01194nam--2200397---450- 001 990000542620203316 005 20090213114154.0 010 $a88-464-3000-X 035 $a0054262 035 $aUSA010054262 035 $a(ALEPH)000054262USA01 035 $a0054262 100 $a20010704d2001----km-y0itay0103----ba 101 0 $aita 102 $aIt 105 $a||||||||001yy 200 1 $a<> mercati del petrolio e la loro volatilità$fFabio Di Benedetto 210 $aMilano$cFranco Angeli$dcopyr. 2001 215 $a169 p.$d23 cm 225 2 $aUniversità$v27 410 0$12001$aUniversità$v27 606 $aPetrolio$xCommercio internazionale 606 $aPetrolio$xEconomia 676 $a338.27 700 1$aDI BENEDETTO,$bFabio$0546290 801 0$aIT$bsalbc$gISBD 912 $a990000542620203316 951 $a338.27 DIB 1 (IEP I 216)$b9568 E.C.$cIEP I$d00075894 959 $aBK 969 $aECO 979 $aCHIARA$b40$c20010704$lUSA01$h1331 979 $c20020403$lUSA01$h1703 979 $aPATRY$b90$c20040406$lUSA01$h1638 979 $aRSIAV2$b90$c20090213$lUSA01$h1141 996 $aMercati del petrolio e la loro volatilità$9885965 997 $aUNISA LEADER 04902nam 22006495 450 001 9910300533903321 005 20200706042205.0 010 $a3-319-78732-2 024 7 $a10.1007/978-3-319-78732-9 035 $a(CKB)4100000003359609 035 $a(MiAaPQ)EBC5355975 035 $a(DE-He213)978-3-319-78732-9 035 $a(PPN)226697584 035 $a(EXLCZ)994100000003359609 100 $a20180420d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApproximate Quantum Markov Chains /$fby David Sutter 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (124 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v28 311 $a3-319-78731-4 327 $aIntroduction -- Classical Markov chains -- Quantum Markov chains -- Outline -- Preliminaries -- Notation -- Schatten norms -- Functions on Hermitian operators -- Quantum channels -- Entropy measures -- Background and further reading -- Tools for non-commuting operators -- Pinching -- Complex interpolation theory -- Background and further reading -- Multivariate trace inequalities -- Motivation -- Multivariate Araki-Lieb-Thirring inequality -- Multivariate Golden-Thompson inequality -- Multivariate logarithmic trace inequality -- Background and further reading -- Approximate quantum Markov chains -- Quantum Markov chains -- Sufficient criterion for approximate recoverability -- Necessary criterion for approximate recoverability -- Strengthened entropy inequalities -- Background and further reading -- A A large conditional mutual information does not imply bad recovery -- B Example showing the optimality of the Lmax-term -- C Solutions to exercises -- References -- Index. 330 $aThis book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple matrix inequality can be extended to more than three matrices. Finally, we carefully discuss the properties of approximate quantum Markov chains and their implications. The book is aimed to graduate students who want to learn about approximate quantum Markov chains as well as more experienced scientists who want to enter this field. Mathematical majority is necessary, but no prior knowledge of quantum mechanics is required. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v28 606 $aQuantum theory 606 $aMathematical physics 606 $aCondensed matter 606 $aStatistical physics 606 $aQuantum computers 606 $aSpintronics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aCondensed Matter Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P25005 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aQuantum Information Technology, Spintronics$3https://scigraph.springernature.com/ontologies/product-market-codes/P31070 615 0$aQuantum theory. 615 0$aMathematical physics. 615 0$aCondensed matter. 615 0$aStatistical physics. 615 0$aQuantum computers. 615 0$aSpintronics. 615 14$aQuantum Physics. 615 24$aMathematical Physics. 615 24$aCondensed Matter Physics. 615 24$aStatistical Physics and Dynamical Systems. 615 24$aQuantum Information Technology, Spintronics. 676 $a519.233 700 $aSutter$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0833856 906 $aBOOK 912 $a9910300533903321 996 $aApproximate Quantum Markov Chains$91864306 997 $aUNINA