Unitary t-designs

In this talk, we introduce the concept of unitary t-designs. A unitary design is a finite set of unitary matrices that nicely approximates the en- tire unitary group, much as spherical design approximates the unit sphere. Unitary t-designs were introduced by Dankert, Cleve, Emerson, and Livine in 2006, and in 2007 Scott showed that unitary t-designs serve as optimal choices for quantum process tomography. Using representations of the unitary group, we give a Delsarte-style lower bound on the size of a unitary t-design and some necessary conditions for the bound to be tight. This is Unijoint work with Andrew Scott.