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Applications of semi-definite optimization in quantum information protocols

Abstrakt

This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information sci- ence. Our results of the analysis of certain quantum information protocols using this optimization technique are presented, and an implementation of a relevant numerical tool is introduced. The key method used is NPA discovered by Navascues et al. [Phys. Rev. Lett. 98, 010401 (2007)]. In chapter 1 a brief overview of mathematical methods used in this work is presented. In chapter 2 an introduction to quantum information science is given. Chapter 3 concerns the device-independent (DI) and semi-device-independent (SDI) approaches in quantum cryptography. In chapter 4 our results regarding quantum information protocols which we developed using SDP are described. The results include a new type of quantum key distribution protocol based on Hardy's paradox; several pro- tocols for quantum random number expansion; a method of formulation of SDP relaxations of SDI protocols; and a DI Santha-Vazirani source of randomness amplification protocol. In chapter 5 an introduction to in- terior point methods is given. In chapter 6 the implementation of our numerical tool dedicated to problems occurring in chapter 4 are discussed and compared with other solutions.

Piotr Andrzej Mironowicz. (2016). Applications of semi-definite optimization in quantum information protocols, 1-230.

Informacje szczegółowe

Kategoria:
Doktoraty, rozprawy habilitacyjne, nostryfikacje
Typ:
praca doktorska pracowników zatrudnionych w PG oraz studentów studium doktoranckiego
Język:
angielski
Rok wydania:
2016

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