Numerical investigation of the effect of hardware parameters on atomic-ensemble-based repeater protocols

Abstract

We perform a numerical optimisation of the hardware parameters of an atomic-ensemble-based single repeater setup. The setup operates on a real-life fiber network connecting the cities Delft and Eindhoven. Besides this network, the setup encompasses photon pair sources, quantum memories, single photon detectors, and 50:50 beam splitters. The corresponding hardware parameters we consider are the following;
- The detector efficiency, defined as the probability the photon detector correctly registers an incident photon.
-The detector dark count probability, defined as the probability that a detector registers a false detection event.
- The memory efficiency, defined as the maximum probability that an excitation is not lost in the quantum memory.
- The memory coherence time, defined as the characteristic time after which an excitation is lost in the quantum memory.
- The Hong-Ou-Mandel visibilty, which is a measure of the indistinguishability of the photons in the setup.
Additionally, the setup has the ability to be multiplexed. This means that the probabilistic processes essential for executing the repeater protocol are initiated $M$ times in parallel. This increases the performance of the protocol.

To achieve the optimisation, we introduce absolute minimal hardware requirements and minimal hardware requirements. An absolute minimal hardware requirement is defined as the least favourable hardware parameter that still allows the setup to reach a given target metric. This implies that all other hardware parameters are at their optimal value. Minimal hardware requirements are defined as the least favourable set of hardware parameters that still allow the setup to reach a given target metric.

To evaluate the aforementioned target metric we conduct a numerical analysis. This analysis is based on the entanglement based version of quantum key distribution. We use Netsquid, a discrete event simulator for quantum networks, to carry out the numerical analysis. Utilising this, we formulate an optimisation problem that allows us to find absolute minimal hardware requirements and minimal hardware requirements for an atomic-ensemble-based single repeater setup.

We develop a method to solve this optimisation problem. This allows us to find absolute minimal hardware requirements and minimal hardware requirements for the hardware parameters listed above. We do this for different number of multiplexing modes, and different node placements on the existing fiber network. We consider both perfect photon pair sources and a model of a photon pair source based on Spontaneous Parametric Down Conversion (SPDC).