Hi all,
it looks like K51 is free, so we'll meet there.
Best,
-joe
On Tue, Apr 11, 2017 at 8:55 AM, Joe Renes joerenes@gmail.com wrote:
Hi all,
we settled on Wednesday at 2pm for Richard's talk. See below for the abstract and relevant papers.
Best,
-joe
Title: Breaking the 4-design barrier: a graceful failure
Abstract:
A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information theory -- one frequently encounters constructions that rely on matrices drawn uniformly at random from the unitary group. Often, it suffices to sample these matrices from a unitary t-design, for sufficiently high t. This results in more explicit, derandomized constructions. The most prominent unitary t-design considered in quantum information is the multi-qubit Clifford group. It is known to be a unitary 3-design, but, unfortunately, not a 4-design. Here, we give a simple, explicit characterization of the way in which the Clifford group fails to constitute a 4-design. Our results show that for various applications in quantum information theory and in the theory of convex signal recovery, Clifford orbits perform almost as well as those of true 4-designs.
Preprints:
https://arxiv.org/abs/1609.08172