Unital quantum channels, majorization and Nielsen's theorem

Postgraduate Thesis uoadl:2940117 24 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2021-03-25
Year:
2021
Author:
Karimali Argyro
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
Languages:
Greek
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 eciently. 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 dene the notion of Purication 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
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
13
Number of pages:
105
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