Blackbox Optimization for Free-space Quantum Key Distribution

Abstract

The Quantum Encryption and Science Satellite is an experimental proof-of-concept of free-space quantum key distribution.

As part of the mission conception, it is imperative to have an optimal design of all elements of the communication protocol. That is, given all of the possible parameters, we ask which combination will achieve the most secure link? This thesis explores the answer to this question for some specific parameters.

A detailed model of the mission is simulated in MATLAB to obtain data points describing the security of the link over the possible set of parameter values. Then, applying appropriate optimization algorithms, we seek to maximize the key rate and minimize the quantum bit error rate. Mathematically, this task reduces to an optimization problem where the objective is a 2-tuple of key rate and quantum bit error rate, which are indicators of protocol security; and the search space is the set of parameter values input to the simulation. The MATLAB simulation cannot be described analytically and thus represents an oracle or blackbox objective function.

In this thesis, a comparison of optimization protocols is conducted between Mesh Adaptive Direct Search (MADS), and Model-based Trust Region (MBTR) methods.

The investigation of optimization algorithm performance is applied to a subset of real Quantum EncrYption and Science Satellite (QEYSSat) parameters: excess voltage supplied to the detectors, and the mean photon number per pulse for the signal.