Entropy of quantum channel in the theory of quantum information

dc.abstract.enQuantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting with an environment. The thesis contains an analysis of properties of quantum channels and different entropies used to quantify the decoherence introduced into the system by a given operation. Part I of the thesis provides a general introduction to the subject. In Part II, the action of a quantum channel is treated as a process of preparation of a quantum ensemble. The Holevo information associated with this ensemble is shown to be bounded by the entropy exchanged during the preparation process between the initial state and the environment. A relation between the Holevo information and the entropy of an auxiliary matrix consisting of square root fidelities between the elements of the ensemble is proved in some special cases. Weaker bounds on the Holevo information are also established. The entropy of a channel, also called the map entropy, is defined as the entropy of the state corresponding to the channel by the Jamiołkowski isomorphism. In Part III of the thesis, the additivity of the entropy of a channel is proved. The minimal output entropy, which is difficult to compute, is estimated by an entropy of a channel which is much easier to obtain. A class of quantum channels is speciffied, for which additivity of channel capacity is conjectured. The last part of the thesis contains characterization of Davies channels, which correspond to an interaction of a state with a thermal reservoir in the week coupling limit, under the condition of quantum detailed balance and independence of rotational and dissipative evolutions. The Davies channels are characterized for one-qubit and one-qutrit systems.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.advisorŻyczkowski, Karol - 132981 pl
dc.contributor.authorRoga, Wojciech - 135131 pl
dc.contributor.institutionJagiellonian University. M. Smoluchowski Institute of Physics. Atomic Optics Departmentpl
dc.contributor.reviewerHorodecki, Michałpl
dc.contributor.reviewerZakrzewski, Jakub - 100023 pl
dc.description.accesstimew momencie opublikowania
dc.description.additionalBibliogr. s. 93-99pl
dc.description.physical[2], 99pl
dc.description.versionostateczna wersja autorska (postprint)
dc.identifier.callnumberDokt. 2011/188pl
dc.identifier.projectROD UJ / OPpl
dc.rights.simpleviewWolny dostęp
dc.share.typeotwarte repozytorium
dc.subject.enquantum channelpl
dc.subject.enHolevo informationpl
dc.subject.plkanał kwantowypl
dc.subject.plinformacja Holevopl
dc.titleEntropy of quantum channel in the theory of quantum informationpl
dc.title.alternativeEntropia kanału kwantowego w teorii informacji kwantowejpl

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