title: A Quantum Hub for Star-Shaped Quantum Key Distribution Networks
Creators: name: Fitzke, Erik
Publisher: name: UNSPECIFIED
Year: 2024

description: Recent advances in the field of classical computing and quantum computing enable new attacks on today's public-key cryptography. Therefore, an essential goal of cybersecurity research is to develop new, future-proof cybersecurity solutions.

Quantum key distribution (QKD) is a method to distribute symmetric digital cryptographic keys between two users by using principles of quantum physics, enabling the information-theoretically secure exchange of encrypted messages. Fundamental principles of quantum physics ensure that the QKD users detect every attempt by a third party to obtain a copy of the key.
However, for many applications, secure connections between two users are insufficient, so larger networks for multiple users are required. On the way to the widespread use of QKD, laboratory experiments under controllable environmental conditions are only the first step, and tests under realistic operating conditions are required to demonstrate the reliability of the systems.

Therefore, the goals of the research presented in this thesis are to develop a multi-user QKD network, to demonstrate its reliability and flexibility in a field test, and to develop detailed models of this system taking the relevant setup imperfections into account.

The multi-user QKD network is implemented as a star-shaped network with a central quantum key hub (q-hub), enabling simultaneous and independent distribution of quantum keys to multiple pairs of users with distances up to 100 km between the users.
In contrast to other QKD networks, the q-hub system uses a polarization-insensitive QKD protocol based on quantum-entangled photon pairs in combination with wavelength demultiplexing to enable robust key transmissions. Therefore, the q-hub system is well suited to implement QKD networks in urban areas or for other applications where the optical fiber transmission links are exposed to the weather or vibrations which may lead to polarization instabilities. 

The first part of this thesis presents the implementation and performance evaluation of a q-hub network with four users. The QKD receivers of the users are synchronized with a precision better than 100 ps by using a new method for clock recovery from the arrival times of the photons for which a patent is pending. 
The compactness and flexibility of the QKD system required for real-world applications are proven in a field test at a facility of the Deutsche Telekom company. This field test was the first field test of a multi-user QKD network based on the Bennett-Brassard-Mermin 1992 (BBM92) time bin QKD protocol. 
Stable key distribution over more than three days is demonstrated for fiber lengths of more than 100 km between two users, including 27 km of fiber deployed in the field. Dozens of users could be readily connected to the network if the required number of QKD receivers were built. 
Finally, a photonic integrated circuit is designed as a first step towards an even more compact q-hub, and on-chip photon pair generation is demonstrated.

The second part of this thesis presents detailed numerical models of the q-hub system.
A new method for the time-dependent tomographic characterization of single-photon detectors in terms of positive operator-valued measures (POVMs) is presented and applied to characterize the detectors employed in the QKD system.

Furthermore, a general method for the photon-number-resolved simulation of multi-mode quantum-optical setups with Gaussian states is developed. A key result is the derivation of the generating function for the photon statistics, from which the photon number distribution and its moments and factorial moments are computed by automatic differentiation. One of the strengths of this simulation method is the flexibility to include effects from various kinds of setup imperfections in simulations of quantum-optical setups. 

Finally, a frequency-resolved simulation of the QKD system is developed by generalizing the covariance formalism of Gaussian states to a continuum of frequencies. 
The simulation results match the measurements to a high degree, allowing for a realistic prediction of the setup performance. The simulation will enable performance optimizations and cost reductions for the development of future QKD networks.