HENRY WOLKOWICZ

(University of Waterloo)

Robust Interior Point Methods for Quantum Key Rate Computation for
Quantum Key Distribution

Abstract. We use facial reduction on the nonlinear objective function and derive a stable reformulation of
the quantum key rate for finite dimensional quantum key distribution (QKD) problems. This avoids the
difficulties for current algorithms from singularities that arise due to loss of positive definiteness for the
distributions. 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.
Empirical evidence illustrates the strength of this approach as we obtain high accuracy solutions and
theoretically guaranteed upper and lower bounds for QKD. We compare with other current approaches in the
literature.

Joint work with: Hao Hu, Jiyoung Im, Jie Lin, Norbert Lutkenhaus.