Title: Robust Interior Point Methods for Key Rate Computation in Quantum Key Distribution
|Affliliation:||University of Waterloo|
|Zoom:||Contact Emma Watson|
We study semidefinite programs for computing the key rate in finite dimensional quantum key distribution (QKD) problems. Through facial reduction, we derive a semidefinite program which is robust and stable in the numerical computation. Our program avoids the difficulties for current algorithms from singularities that arise due to loss of positive definiteness. This allows for the derivation of an efficient Gauss-Newton interior point approach. We provide provable lower and upper bounds for the hard nonlinear semidefinite programming problem.
Title: A Spectral Moore Bound for Bipartite Semiregular Graphs
|Affiliation:||University of Waterloo|
|Zoom:||Contact Soffia Arnadottir|
The Moore bound provides an upper bound on the number of vertices of a regular graph with a given degree and diameter, though there are disappointingly few graphs that achieve this bound. Thus, it is interesting to ask what additional information can be used to give Moore-type bounds that are tight for a larger number of graphs. Cioaba, Koolen, Nozaki, and Vermette considered regular graphs with a given second-largest eigenvalue, and found an upper bound for such graphs.