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arXiv:2208.11493

Performance Analysis of Quantum Key Distribution in Underwater Channels

Amir Hossein Fahim Raouf

Published Aug 20, 2022• 4 citations
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Abstract

The current literature on quantum key distribution (QKD) is mainly limited to the transmissions over fiber optic, atmospheric or satellite links and are not directly applicable to underwater environments with different channel characteristics. Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In the first part of this thesis, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As path loss model, we consider a modified version of Beer-Lambert formula which takes into account the effect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. In the second part of this thesis, as a potential solution to overcome range limitations, we investigate a multi-hop underwater QKD where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays which simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of relay-assisted QKD scheme in terms of QBER and SKR in different water types and turbulence conditions. In the last part of this thesis, we investigate the fundamental performance limits of decoy BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. Based on near field analysis, we utilize the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain a lower bound on key generation rate. Based on this bound, we present the performance of decoy BB84 protocol in different water type.

DOI
10.48550/arxiv.2208.11493

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The current literature on quantum key distribution (QKD) is mainly limited to the transmissions over fiber optic, atmospheric or satellite links and are not directly applicable to underwater environments with different channel characteristics. Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In the first part of this thesis, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As path loss model, we consider a modified version of Beer-Lambert formula which takes into account the effect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. In the second part of this thesis, as a potential solution to overcome range limitations, we investigate a multi-hop underwater QKD where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays which simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of relay-assisted QKD scheme in terms of QBER and SKR in different water types and turbulence conditions. In the last part of this thesis, we investigate the fundamental performance limits of decoy BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. Based on near field analysis, we utilize the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain a lower bound on key generation rate. Based on this bound, we present the performance of decoy BB84 protocol in different water type.
The current literature on quantum key distribution is limited mainly to transmissions over fiber optic, atmospheric, or satellite links and is not directly applicable to underwater environments with different channel characteristics. In this paper, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As a path loss model, we consider a modified version of the Beer–Lambert formula, which takes into account the effect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over a turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. Based on the derived bounds, we present the performance of the BB84 protocol in different water types including clear, coastal, and turbid and under different atmospheric conditions such as clear, hazy, and overcast. We further investigate the effect of system parameters such as aperture size and detector field of view on QBER and SKR performance metrics.
Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In this paper, as a potential solution to overcome range limitations, we investigate a multi-hop underwater quantum key distribution (QKD) where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays that simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of a relay-assisted QKD scheme in terms of quantum bit error rate and secret key rate in different water types and turbulence conditions. We further investigate the effect of system parameters such as aperture size and detector field of view on the performance. Our results demonstrate under what conditions relay-assisted QKD can be beneficial and what end-to-end transmission distances can be supported with a multi-hop underwater QKD system.
Decoy state quantum key distribution protocols have been studied for atmospheric, fiber, and satellite links; however, those results are not directly applicable to underwater environments with different channel characteristics. In this paper, we investigate the fundamental performance limits of decoy state BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. We adopt a near field analysis to determine the average power transfer over a turbulent underwater path and use this to obtain a lower bound on the secret key rate. We quantify the performance of decoy BB84 protocol in different water types assuming various turbulence conditions. We further investigate the effect of system parameters such as transmit aperture size and detector field of view on the performance.
Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communications. In this paper, to overcome range limitations, we investigate a multi-hop underwater quantum key distribution (QKD) where intermediate nodes help the key distribution between the source and destination nodes. We consider deployment of passive-relays which simply redirect the qubits to the next relay node or receiver without any measurement. Based on nearfield analysis, we present the performance of relay-assisted QKD scheme in clear ocean under different atmospheric conditions. We further investigate the effect of system parameters (aperture size and detector field-of-view) on the achievable distance.
This study compares the quantum bit error rate (QBER) performance of BB84, SARG04, and the entanglement-based BBM92 protocol in non-turbulent underwater optical channels. Clear, coastal, and turbid water types are considered under different background-illumination and receiver configurations. For BB84 and SARG04, channel attenuation and background-induced detections determine the quantum gain and QBER. For BBM92, photon loss is included through the two arm detection efficiencies, whereas the polarization state conditioned on two-photon detection is described by local depolarizing Kraus channels. The BBM92 QBER is obtained from the correlations in both measurement bases and from an exact partition of recorded events into true and false coincidences. Stochastic numerical estimates provide consistency checks of the analytical implementation. The results show that water turbidity and optical background reduce the distance below the adopted QBER threshold. They also show that a low conditional BBM92 QBER may coexist with a very small coincidence probability; therefore, the QBER-threshold distance alone does not represent a complete operational or secret-key-rate bound.
In the context of secure underwater optical communications, this study examines the performance of the entanglement-based BBM92 protocol when the source generates non-maximally entangled photon pairs. The impact of seawater optical properties, as well as source correlation characteristics, on transmission efficiency is analyzed for three types of nonturbulent channels: clear, coastal, and turbid water. The main performance metrics, including quantum bit error rate (QBER), secret key rate (SKR), and correlation probability, are analytically derived and evaluated as functions of transmission distance between two communicating parties. Monte Carlo simulation results validate our analytical models and quantify performance under different channel conditions.