Quantum Coin Flipping
and Circuit Design Problems in Distributed Quantum Computing
R. van Houte (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Karen Aardal – Mentor (TU Delft - Discrete Mathematics and Optimization)
D de Laat – Mentor (TU Delft - Discrete Mathematics and Optimization)
Serge Fehr – Graduation committee member (Centrum Wiskunde & Informatica (CWI))
T. Attema – Mentor (TNO)
Joost Bosman – Graduation committee member (TNO)
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Abstract
Quantum coin flipping is a cryptographic primitive in which two or more parties that do not trust each other want establish a fair coin flip. These parties are not physically near each other and use quantum communication channels to interact. A quality of protocols is measured by the best possible cheating strategy, which is the solution of a complex semidefinite optimization problem. In this master thesis we show new explicit bounds in multiparty quantum coin flipping, we investigate how to explicitly formulate these problem in a standard form, we show that a fair coin flip results in the lowest possible bias and we determine more measures of the quality of a protocol. Furthermore, this master thesis presents a rigorous and detailed mathematical description of semidefinite optimization, quantum information theory and quantum coin flipping. This thesis also includes an article written together with J. Mulderij, T. Attema, I. Chiscop and F. Phillipson on distributed quantum computing. In this article, we pose new questions and formulate integer linear programs that solve to find optimal assignment of qubits to computers for a given network of quantum computers and quantum algorithm.