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arXiv:2207.04146 · IEEE Transactions on Communications

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

Dunbar Birnie, Christopher Cheng, Emina Soljanin

Published Feb 22, 2023• 3 citations
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Abstract

We develop new methods of quantifying the impact of photon detector imperfections on possible secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and dark photon counts and show how each may decrease the maximum achievable secret key rate differently. 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. One of our main results is providing tooling for experimentalists to predict their systems’ achievable secret key rate given the detector specifications.

DOI
10.1109/tcomm.2023.3244244

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We develop new methods of quantifying the impact of photon detector imperfections on possible secret key rates in Time-Entanglement based Quantum Key Distribution (QKD). We address photon detection timing jitter, detector downtime, and dark photon counts and show how each may decrease the maximum achievable secret key rate differently. 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. One of our main results is providing tooling for experimentalists to predict their systems’ achievable secret key rate given the detector specifications.
In time entanglement-based quantum key distribution (TE-QKD), Alice and Bob extract the raw key bits from the arrival times of entangled photon pairs. Each entangled pair can contribute to multiple key bits depending on how precisely Alice and Bob can measure the photon arrival times. Thus, TE-QKD can potentially increase the secret key rate compared to typical QKD implementations, which extract up to a bit per photon. Because of entanglement, the times of photon arrivals at Alice’s and Bob’s detectors and, thus, their raw keys should be identical. However, practical photon detectors suffer from time jitter errors. These errors cause discrepancies between Alice’s and Bob’s raw keys. Therefore, Alice must send information to Bob through the public channel to reconcile their raw keys. The amount of data sent for reconciliation represents a loss, rendering secret keys shorter than the raw keys. We compute the secret key rates possible in systems with detector jitter errors and show that they are much higher than those achievable in polarization entanglement-based QKD. We then construct codes for information reconciliation to approach these rates. We demonstrate that short and moderate-length standard error-correcting codes represent excellent information reconciliation choices, making TE-QKD a promising technology.
Abstract In this paper, we theoretically and experimentally study the performance of an entanglement-based quantum key distribution (QKD) system using single-photon detectors (SPDs) with poor afterpulse characteristics. We reveal that the afterpulse fraction ( P a ) in an SPD does not impose a bound on the lowest limit of the error rate in sifted keys of an entanglement-based QKD system. Secure secret key sharing is possible even when P a is large, for example, exceeding 100%. The system performance in terms of the final key rate is found to be dominated by the parameter η/(1 + P a ) of the SPD, where η is the detection efficiency. The operation conditions of the SPD should be optimized so as to have the maximal η/(1 + P a ), while retaining sufficiently low dark counts. The experimental results were in good agreement with the theoretical predictions. A visibility of 90%, which is sufficiently high for secure secret key sharing in a QKD protocol, was obtained in twofold interference experiments even by using an SPD with P a exceeding 100%.
Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secret key generation rates per quantum memory. The two schemes under investigation are the one proposed by Duan et al. [Nature (London) 414, 413 (2001)] and that of Sangouard et al. [Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfection in both protocols, such as nonzero double-photon probabilities at the sources, dark counts in detectors, and inefficiencies in the channel, photodetectors, and memories. We also consider memory decay and dephasing processes in our analysis. For the latter system, we determine the maximum value of the double-photon probability beyond which secret key distillation is not possible. We also find crossover distances for one nesting level to its subsequent one. We finally compare the two protocols in terms of their achievable secret key generation rates at their optimal settings. Our results specify regimes of operation where one system outperforms the other.
One of the key issues in QKD is the rather limited data rate at which the secret key can be generated. This paper explores the use of quantum correlation associated with twin beams in Parametric Down Conversion (PDC) to in effect create a number of parallel channels for generation of secret keys, thus significantly boosting the achievable key rate. Such quantum correlations have been effectively used as a tool for many applications, including calibration of single photon detectors and QKD applications.1 Within QKD applications, the natural setup of quantization of Charge Coupled Device (CCD) detection areas and subsequent measurement of the correlation statistic needed to detect the presence of the eavesdropper Eve, leads to a set of QKD parallel channel models that are either binary or multilevel Discrete Memoryless Channels (DMC). This work explores the derivation of proper channel models for this application starting from measured data and the optimization of the secret key rate. Analytical results based on measurements performed on a 30 pixel image suggest that nearly an 8-fold increase in secret key rate may be achievable using this technique.
We theoretically analyse the relation between non-Gaussianity and security of entanglement-based quantum key distribution (QKD) protocols, namely device-independent (DI) and entanglement-based BB848484. A similar analysis has already been made for prepare-and-measure (P\&M) protocols \cite{Lasota2017}. In addition, we consider imperfect detection with dark counts and limited efficiency. We assume a perfect source of entangled Bell states as produced by quantum-dot type sources, depolarisation in the channel and different noise statistics, namely thermal and Poissonian. We consider single-photon avalanche photodiodes (SPAD) and photon number resolving detectors (PNRD) and use their respective criteria for non-Gaussianity. The results show cross-regions for both security and non-Gaussianity, hence, the possibility to conclude about the suitability of a given channel for secret key distribution. Our results can be useful as a pre-check for the implementation of QKD protocols.
Pulse-position modulation (PPM) is a promising technique that can be used to improve the efficiency of quantum key distribution (QKD) based on a Poisson photon source. In this paper, we first investigate a simple entanglement-and- PPM-based QKD protocol and demonstrate the improvement in secret key rate. However, such a PPM-based QKD protocol that utilizes only frames with a single click is still inefficient because it ignores frames with two and more clicks. For this reason we propose to use such multi-click frames to further improve the efficiency of PPM-based QKD by employing a better sifting strategy. Specifically, we focus on using the frames with two clicks in addition to those with a single click. Finally, we analyze the secret key rate under various noise levels in the scenario of high channel loss, which has been faced by most QKD applications. With the analytical results, we show the advantage of the proposed PPM-based QKD.