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978-3-8439-1152-8, Reihe Physik

Ulrich Seyfarth Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption

158 Seiten, Dissertation Technische Universität Darmstadt (2013), Hardcover, B5

Mutually unbiased bases (MUBs) find their applications in the fields of quantum state estimation and quantum key distribution. By their relation to mathematical objects like orthogonal Latin squares or symplectic spreads, considerations result in immediate effects in these fields. Many (even fundamental) questions on MUBs are still unsolved. What we treat in this work is the problem of explicitly constructing cyclic MUBs in a straightforward way. These bases have advantages in theoretical tasks as well as in experimental implementations and provide a reduced formulation of a concrete set of MUBs. A relation to an open conjecture given by Wiedemann 1988 in finite field theory is discovered and serves a realization of this conjecture which may lead to a proof, as well as a recursive construction of cyclic MUBs in an infinite subset of the dimensions. The algorithmical formulation of an implementation strategy leads to feasible implementations. Approaches to prove the conjecture of Wiedemann, a positive test of the conjecture for the first ten applications of a doubling scheme (which is limited by the largest known prime-number factorization of Fermat numbers) and resulting complete sets of cyclic MUBs for systems with up to 600 qubits complete the considerations.

The second part of this work deals with the security of a recently discussed quantum public-key encryption scheme.