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Title: A study on mutually unbiased bases
Authors: LU XIN
Keywords: MUB, finite fields, unbiasedness , Hadamard matrices, rotor, Heisenberg pair
Issue Date: 18-May-2012
Citation: LU XIN (2012-05-18). A study on mutually unbiased bases. ScholarBank@NUS Repository.
Abstract: Various problems of existence of maximal sets of mutually unbiased bases are studied. For finite dimensional spaces, the well-known construction in prime power dimensions is reviewed in a systematic way, followed by an application in quantum dynamics. Next, in dimension six, we perform a numerical search and obtain the analytical expression of the four bases that have the highest?unbiasedness? found in the search. Our result provides another evidence that we can at most have a set of three mutually unbiased bases in dimension six. For infinite dimensional spaces, the continuous degree of freedom of the rotor is studied. A suitable Heisenberg pair of complementary observables is constructed. In this way, we provide a continuous set of mutually unbiased bases for the rotor and show that the rotor degree of freedom is on equal footing with the other continuous degrees of freedom.
Appears in Collections:Ph.D Theses (Open)

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