Year: 2008
Type: dissertation
Abstract: In this thesis we investigate complete systems of MUBs and SIC-POVMs. These are highly \nsymmetric sets of vectors in Hilbert space, interesting because of their applications in quantum \ntomography, quantum cryptography and other areas. It is known that these objects \nform complex projective 2-designs, that is, they satisfy Welch bounds for k = 2 with equality. \nUsing this fact, we derive a necessary and sufficient condition for a set of vectors to be \na complete system of MUBs or a SIC-POVM. This condition uses the orthonormality of a \nspecific set of vectors. \nThen we define homogeneous systems, as a special case of systems of vectors for which \nthe condition takes an especially elegant form. We show how known results and some new \nresults naturally follow from this construction.
Source: UWSpace (University of Waterloo)
Author: Aleksandrs Belovs
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: University of Waterloo
OpenAlex ID: W1202412312