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" Quantum entanglement in non-local games, graph parameters and zero-error information theory "
Giannicola Scarpa.
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BL
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| Record Number
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772192
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b592185
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Giannicola Scarpa.
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| Title & Author
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Quantum entanglement in non-local games, graph parameters and zero-error information theory\ Giannicola Scarpa.
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| Publication Statement
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Amsterdam : ILLC ; Amsterdam : Universiteit van Amsterdam [Host], 2013
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| Series Statement
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ILLC dissertation series, DS-2013-03
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(Text. :) ill.
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| ISBN
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9061965667
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: 9789061965664
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Met samenvatting in het Nederlands.
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| Abstract
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We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory. In Chapter 2 we address the question of how much quantum correlations generated by entanglement can deviate from classical predictions. We focus on non-local games: experiments in which two players are separated and forbidden to communicate, and have to collaborate to accomplish a task. We give two games exhibiting quantum-classical separations close to optimal. Remarkably, our results in theoretical physics are inspired by theoretical computer science. Chapter 3 is dedicated to the study of quantum graph parameters. Well-known quantities such as the chromatic number and the independence number of a graph can be interpreted as parameters for non-local games. A definition of quantum graph parameters follows from this fact. We contribute to the field in a number of ways. Among other results, we find a surprising characterization of the quantum chromatic number that relates to the Kochen-Specker theorem, a result in the foundations of quantum mechanics. In Chapter 4, we move to zero-error information theory. We study the zero error capacity of a classical noisy channel when the sender and the receiver can use quantum entanglement. We initiate the study of the source problem and source-channel problem with entanglement and we find channels and sources that exhibit a strong divergence in quantum and classical behaviours. To do that, we use results in combinatorics, linear algebra, optimization and number theory.--Samenvatting auteur.
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Giannicola Scarpa
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