Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Μιχαήλ Ανούσης, Καθηγητής, Τμήμα Μαθηματικών, Πανεπιστήμιο του Αιγαίου
Απόστολος Γιαννόπουλος, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Αριστείδης Κατάβολος, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Μοναδιαία κβαντικά κανάλια, κυριαρχία και το θεώρημα του Nielsen
Translated title:
Unital quantum channels, majorization and Nielsen's theorem
Summary:
In this thesis we present some key topics of interest pertaining to the Theory of Quantum Information. The Theory of Quantum Information studies how quantummechanical properties of physical systems can be utilized, in order to carry o storage and transmission of information more e ciently. The emphasis in this Thesis is on Quantum Channels and the Majorization Theory. The key terms that needed for studying Quantum Channels, as well as the notation being used, are all mentioned in Chapter 2. Chapter 3 presents Registers and their states. Additionally, we de ne the notion of Puri cation of states and study conditions for its existence. Some key elements of the Theory of Quantum Channels are being explored in Chapter 4. Properties and representations of Quantum Channels are also studied in this Chapter. Furthermore, we present various categories of Quantum Channels such as Unital Channels, Mixed Unitary Channels, Completely Dephasing Channels, Replacement Channels, Schur Channels, Weyl-covariant Channels and the Completely Depolarizing Channel. In Chapter 5, we study the notion of Majorization for real vectors and for Hermitian operators. We also formulate and prove Nielsen's theorem.
Main subject category:
Science
Keywords:
Registers, Quantum states, Quantum channels, majorization
