Unitary design: bounds on their size
APA
Scott, A. (2008). Unitary design: bounds on their size. Perimeter Institute. https://pirsa.org/08100071
MLA
Scott, Andrew. Unitary design: bounds on their size. Perimeter Institute, Oct. 27, 2008, https://pirsa.org/08100071
BibTex
@misc{ pirsa_PIRSA:08100071, doi = {10.48660/08100071}, url = {https://pirsa.org/08100071}, author = {Scott, Andrew}, keywords = {Quantum Information, Quantum Foundations}, language = {en}, title = {Unitary design: bounds on their size}, publisher = {Perimeter Institute}, year = {2008}, month = {oct}, note = {PIRSA:08100071 see, \url{https://pirsa.org}} }
Griffith University
Talk Type
Abstract
As a means of exactly derandomizing certain quantum information processing tasks, unitary designs have become an important concept in quantum information theory. A unitary design is a collection of unitary matrices that approximates the entire unitary group, much like a spherical design approximates the entire unit sphere. We use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t. The tightness of these bounds is then considered, where specific unitary 2-designs are introduced that are analogous to SIC-POVMs and complete sets of MUBs in the complex projective case. Additionally, we catalogue the known constructions of unitary t-designs and give an upper bound on the size of the smallest weighted unitary t-design in U(d). This is joint work with Aidan Roy (Calgary): \'Unitary designs and codes,\' arXiv:0809.3813.