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/1609.08172https://arxiv.org/abs/1609.08595https://arxiv.org/abs/1610.08070
Hi all,
today Martin Lickteig will tell us about the results of his master's
thesis, which is concerned with resource theory and noisy operations
in thermodynamics.
Best,
-joe