Please use this identifier to cite or link to this item:
https://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 | 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. | URI: | http://scholarbank.nus.edu.sg/handle/10635/35578 |
Appears in Collections: | Ph.D Theses (Open) |
Show full item record
Files in This Item:
File | Description | Size | Format | Access Settings | Version | |
---|---|---|---|---|---|---|
LuXin.pdf | 671.78 kB | Adobe PDF | OPEN | None | View/Download |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.