Abstract: When studying ''random" operators it is essential to be able to integrate over the Haar measure. Unitary t-designs which have many applications in Quantum information theory provide a method to simplify integrating polynomials of degree less than 't' over U(d) by replacing the averages over haar measure by the averages over a finite set. We see an explicit construction of a 1-design and use it to prove that t-designs are non-commuting.
