Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1903.01218 · Journal of the Optical Society of America A

Performance of underwater quantum key distribution with polarization encoding

Shi-Cheng Zhao, Zhao-Qi-Zhi Han, Ya Xiao, Y. R. Shen, Yongjian Gu, Wendong Li

Published Apr 23, 2019• 35 citations
arXivHTMLPDF

Abstract

Underwater quantum key distribution (QKD) has potential applications in absolutely secure underwater communication. However, the performance of underwater QKD is limited by the optical elements, background light, and dark counts of the detector. In this paper, we propose a modified formula for the quantum bit error rate (QBER), which takes into account the effect of detector efficiency on the QBER caused by the background light. Then we calculate the QBER of the polarization encoding BB84 protocol in Jerlov-type seawater by analyzing the effect of the background light and optical components in a more realistic situation. Finally, we further analyze the final key rate and the maximum secure communication distance in three propagation modes, i.e., upward, downward, and horizontal modes. We find that secure QKD can be performed in the clearest Jerlov-type seawater at a distance of hundreds of meters, even in the worst downward propagation mode. Specifically, by optimizing the system parameters, it is possible to securely transmit information with a rate of 67 kbits/s at a distance of 100 m in the seawater channel with an attenuation coefficient of 0.03/m at night. For practical underwater QKD, the performance can also be improved by using decoy states. Our results are useful for long-distance underwater quantum communication.

DOI
10.1364/josaa.36.000883

Related papers

Experimental underwater quantum key distribution

Zhao Feng, Shangbin Li, Zhengyuan Xu

In recent years, the feasibility of quantum key distribution (QKD) in a water channel has been verified by theory and experiment. Here, we present an experimental investigation of QKD and decoy-state QKD based on the BB84 protocol. The experiment was carried out in a 10 m water tank. The attenuation coefficient of tap water is 0.08/m, which is close to Jerlov Type II seawater. We measured the probability-of-detection matrix of polarization states, and the average fidelity of the four polarization states is up to 98.39%. For the 10 m underwater QKD experiment, 20 MHz optical pulses are generated by modulating the laser diode (LD) and attenuated to an average of 0.1 photons per pulse. The security key rate can reach 563.41 kbits/s and the quantum bit error rate (QBER) is 0.36%. Two decoy states (one of which is the vacuum state) was used in the 10 m underwater decoy-state QKD experiment, and the average QBER of signal state is 0.95%, the security key rate reaches 711.29 kbits/s. According to the parameters of the decoy-state experiment, the maximum secure transmission distance of the underwater decoy-state QKD is predicted to be 19.2 m, while it can be increased to 237.1 m in Jerlov Type I seawater with a lower dark count single photon detector (SPD).

Optics Express•Feb 23, 2021•59 citations

Practical underwater quantum key distribution based on decoy-state BB84 protocol

Shanchuan Dong, Yonghe Yu, Shangshuai Zheng +4 more

Polarization encoding quantum key distribution has been proven to be a reliable method to build a secure communication system. It has already been used in an inter-city fiber channel and near-Earth atmosphere channel, leaving an underwater channel the last barrier to conquer. Here we demonstrate a decoy-state BB84 quantum key distribution system over a water channel with a compact system design for future experiments in the ocean. In the system, a multiple-intensity modulated laser module is designed to produce the light pulses of quantum states, including signal state, decoy state, and vacuum state. Classical communication and synchronization are realized by wireless optical transmission. Multiple filtering techniques and wavelength division multiplexing are further used to avoid cross talk of different lights. We test the performance of the system and obtain a final key rate of 245.6 bps with an average quantum bit error rate of 1.91% over a 2.4 m water channel, in which the channel attenuation is 16.35 dB. Numerical simulation shows that the system can tolerate up to 21.7 dB total channel loss and can still generate secure keys in 277.9 m Jerlov type I ocean channel.

arXiv:2203.04598•Applied Optics•May 3, 2022•5 citations

Performance Analysis of Quantum Key Distribution in Underwater Channels

Amir Hossein Fahim Raouf

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.

arXiv:2208.11493•Aug 20, 2022•4 citations

Experimental demonstration of underwater decoy-state quantum key distribution with all-optical transmission

Yonghe Yu, Wendong Li, Weidong Yu +8 more

We demonstrate the underwater quantum key distribution (UWQKD) over a 10.4-meter Jerlov type III seawater channel by building a complete UWQKD system with all-optical transmission of quantum signals, a synchronization signal and a classical communication signal. The wavelength division multiplexing and the space-time-wavelength filtering technology are applied to ensure that the optical signals do not interfere with each other. The system is controlled by FPGA and can be easily integrated into watertight cabins to perform the field experiment. By using the decoy-state BB84 protocol with polarization encoding, we obtain a bit rate of secure keys of 1.82 Kbps and an error rate of 1.55% at the attenuation of 13.26 dB. We prove that the system can tolerate the channel loss up to 23.7 dB and therefore may be used in the 300-meter-long Jerlov type I clean seawater channel.

arXiv:2106.13441•Optics Express•Aug 30, 2021•9 citations

Performance Analysis of Underwater Quantum Key Distribution Protocols: BB84, SARG04, and BBM92

Nour Rizk, Angélique Drémeau, Arnaud Coatanhay

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.

quant-pharXiv:2605.29513•May 29, 2026•0 citations

Optimized decoy state QKD for underwater free space communication

Minal Lopes, Nisha Sarwade

Quantum cryptography (QC) is envisioned as a solution for global key distribution through fiber optic, free space and underwater optical communication due to its unconditional security. In view of this, this paper investigates underwater free space quantum key distribution (QKD) model for enhanced transmission distance, secret key rates and security. It is reported that secure underwater free space QKD is feasible in the clearest ocean water with the sifted key rates up to 207[Formula: see text]kbps. This paper extends this work by testing performance of optimized decoy state QKD protocol with underwater free space communication model. The attenuation of photons, quantum bit error rate and the sifted key generation rate of underwater quantum communication is obtained with vector radiative transfer theory and Monte Carlo method. It is observed from the simulations that optimized decoy state QKD evidently enhances the underwater secret key transmission distance as well as secret key rates.

International Journal of Quantum Information•Mar 1, 2018•16 citations
Underwater quantum key distribution (QKD) has potential applications in absolutely secure underwater communication. However, the performance of underwater QKD is limited by the optical elements, background light, and dark counts of the detector. In this paper, we propose a modified formula for the quantum bit error rate (QBER), which takes into account the effect of detector efficiency on the QBER caused by the background light. Then we calculate the QBER of the polarization encoding BB84 protocol in Jerlov-type seawater by analyzing the effect of the background light and optical components in a more realistic situation. Finally, we further analyze the final key rate and the maximum secure communication distance in three propagation modes, i.e., upward, downward, and horizontal modes. We find that secure QKD can be performed in the clearest Jerlov-type seawater at a distance of hundreds of meters, even in the worst downward propagation mode. Specifically, by optimizing the system parameters, it is possible to securely transmit information with a rate of 67 kbits/s at a distance of 100 m in the seawater channel with an attenuation coefficient of 0.03/m at night. For practical underwater QKD, the performance can also be improved by using decoy states. Our results are useful for long-distance underwater quantum communication.
In recent years, the feasibility of quantum key distribution (QKD) in a water channel has been verified by theory and experiment. Here, we present an experimental investigation of QKD and decoy-state QKD based on the BB84 protocol. The experiment was carried out in a 10 m water tank. The attenuation coefficient of tap water is 0.08/m, which is close to Jerlov Type II seawater. We measured the probability-of-detection matrix of polarization states, and the average fidelity of the four polarization states is up to 98.39%. For the 10 m underwater QKD experiment, 20 MHz optical pulses are generated by modulating the laser diode (LD) and attenuated to an average of 0.1 photons per pulse. The security key rate can reach 563.41 kbits/s and the quantum bit error rate (QBER) is 0.36%. Two decoy states (one of which is the vacuum state) was used in the 10 m underwater decoy-state QKD experiment, and the average QBER of signal state is 0.95%, the security key rate reaches 711.29 kbits/s. According to the parameters of the decoy-state experiment, the maximum secure transmission distance of the underwater decoy-state QKD is predicted to be 19.2 m, while it can be increased to 237.1 m in Jerlov Type I seawater with a lower dark count single photon detector (SPD).
Polarization encoding quantum key distribution has been proven to be a reliable method to build a secure communication system. It has already been used in an inter-city fiber channel and near-Earth atmosphere channel, leaving an underwater channel the last barrier to conquer. Here we demonstrate a decoy-state BB84 quantum key distribution system over a water channel with a compact system design for future experiments in the ocean. In the system, a multiple-intensity modulated laser module is designed to produce the light pulses of quantum states, including signal state, decoy state, and vacuum state. Classical communication and synchronization are realized by wireless optical transmission. Multiple filtering techniques and wavelength division multiplexing are further used to avoid cross talk of different lights. We test the performance of the system and obtain a final key rate of 245.6 bps with an average quantum bit error rate of 1.91% over a 2.4 m water channel, in which the channel attenuation is 16.35 dB. Numerical simulation shows that the system can tolerate up to 21.7 dB total channel loss and can still generate secure keys in 277.9 m Jerlov type I ocean channel.
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.
We demonstrate the underwater quantum key distribution (UWQKD) over a 10.4-meter Jerlov type III seawater channel by building a complete UWQKD system with all-optical transmission of quantum signals, a synchronization signal and a classical communication signal. The wavelength division multiplexing and the space-time-wavelength filtering technology are applied to ensure that the optical signals do not interfere with each other. The system is controlled by FPGA and can be easily integrated into watertight cabins to perform the field experiment. By using the decoy-state BB84 protocol with polarization encoding, we obtain a bit rate of secure keys of 1.82 Kbps and an error rate of 1.55% at the attenuation of 13.26 dB. We prove that the system can tolerate the channel loss up to 23.7 dB and therefore may be used in the 300-meter-long Jerlov type I clean seawater channel.
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.
Quantum cryptography (QC) is envisioned as a solution for global key distribution through fiber optic, free space and underwater optical communication due to its unconditional security. In view of this, this paper investigates underwater free space quantum key distribution (QKD) model for enhanced transmission distance, secret key rates and security. It is reported that secure underwater free space QKD is feasible in the clearest ocean water with the sifted key rates up to 207[Formula: see text]kbps. This paper extends this work by testing performance of optimized decoy state QKD protocol with underwater free space communication model. The attenuation of photons, quantum bit error rate and the sifted key generation rate of underwater quantum communication is obtained with vector radiative transfer theory and Monte Carlo method. It is observed from the simulations that optimized decoy state QKD evidently enhances the underwater secret key transmission distance as well as secret key rates.