On the optimization of underwater quantum key distribution systems with time-gated SPADs

Amir Hossein Fahim Raouf; Murat Uysal

doi:10.1364/JOSAB.451237

Journal of the Optical Society of America B
Vol. 39,
Issue 8,
pp. 2013-2019
(2022)
•https://doi.org/10.1364/JOSAB.451237

On the optimization of underwater quantum key distribution systems with time-gated SPADs

Amir Hossein Fahim Raouf and Murat Uysal

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Amir Hossein Fahim Raouf and Murat Uysal, "On the optimization of underwater quantum key distribution systems with time-gated SPADs," J. Opt. Soc. Am. B 39, 2013-2019 (2022)

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Related Topics
Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: December 13, 2021
- Revised Manuscript: May 2, 2022
- Manuscript Accepted: June 9, 2022
- Published: July 7, 2022

Abstract

In this paper, we study the effect of various transmitter and receiver parameters on the quantum bit error rate (QBER) performance of underwater quantum key distribution. We utilize a Monte Carlo approach to simulate the trajectories of emitted photons transmitting in water from the transmitter towards the receiver. Based on propagation delay results, we first determine a proper value for the bit period to avoid intersymbol interference as a result of possible multiple scattering events. Then, based on the angle of arrival of the received photons, we determine a proper field of view to limit the average number of received background noise. Finally, we determine the optimal value for the single photon avalanche diode gate time in the sense of minimizing the QBER for the selected system parameters and given propagation environment.

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Parameter	Definition	Numerical Value
$r_{0}$	Transmitter beam width	3 mm [25]
$θ_{0, max}$	Maximum beam divergence	20° [25]
$Δ λ$	Filter spectral width	30 nm [22]
$λ$	Wavelength	532 nm [22]
$d$	Receiver aperture diameter	20 cm [25]
$I_{dc}$	Dark current count rate	60 Hz [22]
$K_{\infty}$	Asymptotic diffuse attenuation coefficient	$0.08 m^{- 1}$ [28]
$z_{d}$	Depth	100 m [22]
$R_{d} (λ, 0)$	Irradiance of underwater environment at sea surface	$10^{- 3} W / m^{2}$ [29]
$ς$	Extinction coefficient (clear water)	$0.151 m^{- 1}$ [25]

$r_{0}$ (cm)	$θ_{0, max}$	$L$ (m)	$Δ t$ (ns)	$Ω$	$Δ t^{'}$ (ps)	QBER
0.3	20°	10	1	27°	9	$9.80 \times 10^{- 6}$
		20	3	35°	19	$1.60 \times 10^{- 4}$
		30	5	42°	32	$1.20 \times 10^{- 3}$
		40	8	45°	61	$6.60 \times 10^{- 3}$
3	20°	10	1	30°	8	$1.34 \times 10^{- 5}$
		20	3	35°	20	$2.00 \times 10^{- 4}$
		30	6	44°	38	$1.60 \times 10^{- 3}$
		40	11	47°	66	$9.20 \times 10^{- 3}$
30	20°	10	5	58°	70	$2.80 \times 10^{- 3}$
		20	6	55°	63	$3.10 \times 10^{- 3}$
		30	10	53°	81	$8.20 \times 10^{- 3}$
		40	12	51°	107	$2.10 \times 10^{- 2}$
0.3	0°	10	0.06	18°	3	$8.42 \times 10^{- 7}$
		20	0.16	20°	6	$1.21 \times 10^{- 5}$
		30	0.38	23°	14	$1.25 \times 10^{- 4}$
		40	0.73	26°	25	$8.84 \times 10^{- 4}$
0.3	45°	10	1	27°	8	$9.78 \times 10^{- 6}$
		20	3	37°	17	$1.63 \times 10^{- 4}$
		30	7	44°	39	$1.50 \times 10^{- 3}$
		40	11	48°	66	$9.10 \times 10^{- 3}$

Parameter	Definition	Numerical Value
$r_{0}$	Transmitter beam width	3 mm [25]
$θ_{0, max}$	Maximum beam divergence	20° [25]
$Δ λ$	Filter spectral width	30 nm [22]
$λ$	Wavelength	532 nm [22]
$d$	Receiver aperture diameter	20 cm [25]
$I_{dc}$	Dark current count rate	60 Hz [22]
$K_{\infty}$	Asymptotic diffuse attenuation coefficient	$0.08 m^{- 1}$ [28]
$z_{d}$	Depth	100 m [22]
$R_{d} (λ, 0)$	Irradiance of underwater environment at sea surface	$10^{- 3} W / m^{2}$ [29]
$ς$	Extinction coefficient (clear water)	$0.151 m^{- 1}$ [25]

$r_{0}$ (cm)	$θ_{0, max}$	$L$ (m)	$Δ t$ (ns)	$Ω$	$Δ t^{'}$ (ps)	QBER
0.3	20°	10	1	27°	9	$9.80 \times 10^{- 6}$
		20	3	35°	19	$1.60 \times 10^{- 4}$
		30	5	42°	32	$1.20 \times 10^{- 3}$
		40	8	45°	61	$6.60 \times 10^{- 3}$
3	20°	10	1	30°	8	$1.34 \times 10^{- 5}$
		20	3	35°	20	$2.00 \times 10^{- 4}$
		30	6	44°	38	$1.60 \times 10^{- 3}$
		40	11	47°	66	$9.20 \times 10^{- 3}$
30	20°	10	5	58°	70	$2.80 \times 10^{- 3}$
		20	6	55°	63	$3.10 \times 10^{- 3}$
		30	10	53°	81	$8.20 \times 10^{- 3}$
		40	12	51°	107	$2.10 \times 10^{- 2}$
0.3	0°	10	0.06	18°	3	$8.42 \times 10^{- 7}$
		20	0.16	20°	6	$1.21 \times 10^{- 5}$
		30	0.38	23°	14	$1.25 \times 10^{- 4}$
		40	0.73	26°	25	$8.84 \times 10^{- 4}$
0.3	45°	10	1	27°	8	$9.78 \times 10^{- 6}$
		20	3	37°	17	$1.63 \times 10^{- 4}$
		30	7	44°	39	$1.50 \times 10^{- 3}$
		40	11	48°	66	$9.10 \times 10^{- 3}$

Abstract

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Equations (12)

Journal of the Optical Society of America B