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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Single-photon acquisition probability for free-space quantum key distribution

Guangyu Zhang, Jing Ma, Liying Tan, Siyuan Yu, Qiqi Han, Yunliang Chen

Published Jan 11, 2005• 8 citations
Publisher

Abstract

Two theoretical models of single-photon acquisition probability based on the fundamental-mode Gaussian beam are established for free-space quantum key distribution and are compared in theory and simulation. The parameters that influence the single-photon acquisition probability are the transmitter's tracking-pointing error, the far-field divergence angle, the link distance between the transmitter and receiver and the receiver's antenna aperture. The single-photon acquisition probability is analyzed in the numerical simulation and its orders of magnitude are given for the ground-to-ground, satellite-to-ground and satellite-to-satellite links. The results of the theoretical analysis and the numerical simulation show that it is feasible to acquire single-photon for the satellite-to-ground and satellite-to-satellite quantum key distribution.

DOI
10.1117/12.566152

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Two theoretical models of single-photon acquisition probability based on the fundamental-mode Gaussian beam are established for free-space quantum key distribution and are compared in theory and simulation. The parameters that influence the single-photon acquisition probability are the transmitter's tracking-pointing error, the far-field divergence angle, the link distance between the transmitter and receiver and the receiver's antenna aperture. The single-photon acquisition probability is analyzed in the numerical simulation and its orders of magnitude are given for the ground-to-ground, satellite-to-ground and satellite-to-satellite links. The results of the theoretical analysis and the numerical simulation show that it is feasible to acquire single-photon for the satellite-to-ground and satellite-to-satellite quantum key distribution.
Theoretical model of single photon acquisition probability is established for free-space quantum key distribution.The expression of single photon acquisition probability is deduced from the fundamental-mode Gaussian beam.The parameters that influence the single photon acquisition probability are the transmitter's tracking-pointing error,the far-field divergence angle,the link distance between transmitter and receiver and the receiver's antenna aperture.The single photon acquisition probability is analyzed in numerical simulation for the link between a ground station and a satellite in a low earth orbit and it is normally on the order of 10~(3)~10~(-5).
The expressions of single-photon acquisition probability are deduced from TEM10 mode Laguerre-Gaussian beams. Single-photon acquisition is analyzed for the links between a ground station and a satellite in a low earth orbit. The results show that single-photon can be acquired by the receiver on the satellite at the maximum probability if highly attenuated laser pulses based on TEM10 mode Laguerre-Gaussian beams are used as single-photon sources and a bright precursor reference pulse can be used to set a short time window. Single-photon acquisition probability is normal on the order of 10-1~10-3. In comparison with the fundamental-mode Gaussian beam, the TEM10 mode Laguerre- Gaussian beams have an advantage because the losses of single-photon acquisition probability can not be caused by the satellite movement. Atmospheric turbulence is considered and the expressions of single- photon acquisition probability are modified.
The expressions of single-photon acquisition probability in free-space quantum key distribution were deduced based on TEM10 mode Laguerre-Gaussian beams.The single-photon acquisition was analyzed for the laser link between a ground station and a satellite in a low earth orbit.The results show that single-photon can be acquired by the receiver in the satellite with maximum probability if highly attenuated laser pulses based on TEM10 mode Laguerre-Gaussian beams are used as single-photon sources and a bright precursor reference pulse is used to set a short time window for the single-photon acquisition.Unlike the fundamental-mode Gaussian beam,the TEM10 mode Laguerre-Gaussian beam does not cause the single-photon acquisition probability losses due to the movement of satellites.
Highly attenuated laser pulses with Poisson distribution are used as single-photon sources and the BB84 and B92 protocols are used for free-space quantum key distribution.By introducing the quantum channel transmission,the single-photon acquisition probability,the measuring factor and the sifting factor,the theoretical model of the quantum bit error rate was established and the expressions of the quantum bit error rate were given.The main factors that cause the quantum bit error rate are the optical elements,the detector dark noise and the space optical environment and these factors were analyzed.The quantum bit error rate was analyzed in the numerical simulation for the laser links between a ground station and a satellite in a low earth orbit.The results show that it is feasible to implement quantum key distribution between a ground station and a satellite in a low earth orbit and that it is the detector dark noise and the space optical environment that limit the link distance for free-space quantum key distribution.
Modern optical technology has greatly facilitated the implementation of free-space quantum key distribution. However, the influence of atmosphere on the beam propagation is always unpredictable and could impair the system performance to some extent. It is necessary to develop an efficient model that could describe the beam propagation and receiving. In this paper, a single-photon receiving efficiency model is proposed incorporating the single-photon acquisition probability and channel transmittance based on the Gaussian beam propagation. We also present simulation and experiment of beam-spot size widening through a 0.5 km free-space channel to verify the proposed model. The results show that with the increase of turbulence strengths, the single-photon acquisition probability will degrade more sharply. The single-photon receiving efficiency will decrease with the increment of the ratio between beam centroid deflection and the receiving aperture radius [Formula: see text].
The expressions of the quantum key bit rate are given for free-space quantum key distribution by introducing the quantum channel transmission, the single-photon acquisition probability, the detection factor and the sifting factor. The quantum key bit rate is studied in the numerical simulation for the laser links between a ground station and a satellite in a low earth orbit. The results show that it is feasible to implement quantum key distribution between a ground station and a satellite in a low earth orbit.