PIRSA:08100071  ( MP4 Medium Res , MP3 , PDF ) Which Format?
Unitary design: bounds on their size
Speaker(s): Andrew Scott
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.
Date: 27/10/2008 - 11:30 am
Valid XHTML 1.0!