Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/35578
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
Source: 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.
URI: http://scholarbank.nus.edu.sg/handle/10635/35578
Appears in Collections:Ph.D Theses (Open)

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