Information Rates with Non Ideal Photon Detectors in Time-Entanglement Based QKD

TL;DR

This paper introduces new models to quantify how photon detector imperfections like jitter, downtime, and dark counts impact secret key rates in time-entanglement QKD, providing practical tools for experimental system optimization.

Contribution

It presents novel Markov Chain models and analysis methods to accurately assess the effects of detector imperfections on QKD secret key rates, including dark counts and timing jitter.

Findings

Detector imperfections significantly reduce secret key rates.

Markov Chain model captures detector downtime effects.

Dark counts are especially harmful with Pulse Position Modulation.

Abstract

We develop new methods of quantifying the impact of photon detector imperfections on achievable secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and photon dark counts and show how each may decrease the maximum achievable secret key rate in different ways. We begin with a standard Discrete Memoryless Channel (DMC) model to get a good bound on the mutual information lost due to the timing jitter, then introduce a novel Markov Chain (MC) based model to characterize the effect of detector downtime and show how it introduces memory to the key generation process. Finally, we propose a new method of including dark counts in the analysis that shows how dark counts can be especially detrimental when using the common Pulse Position Modulation (PPM) for key generation. Our results show that these three imperfections can significantly reduce the achievable secret key rate when using PPM for QKD. Additionally, one of our main results is providing tooling for experimentalists to predict their systems' achievable secret key rate given the detector specifications.