Integrating deep learning to achieve phase
compensation for free-space orbital-angular-
momentum-encoded quantum key distribution
under atmospheric turbulence
XINGYU WANG,
1,2
TIANYI WU,
2
CHEN DONG,
2,
*HAONAN ZHU,
1
ZHUODAN ZHU,
3
AND SHANGHONG ZHAO
1
1
School of Information and Navigation, Air Force Engineering University, Xi’an 710077, China
2
Information and Communication College, National University of Defense Technology, Xi’an 710006, China
3
No. 94782 Unit of PLA, Hangzhou 310021, China
*Corresponding author: dongchengfkd@163.com
Received 9 September 2020; revised 17 November 2020; accepted 20 November 2020; posted 22 November 2020 (Doc. ID 409645);
published 13 January 2021
A high-dimensional quantum key distribution (QKD), which adopts degrees of freedom of the orbital angular
momentum (OAM) states, is beneficial to realize secure and high-speed QKD. However, the helical phase of a
vortex beam that carries OAM is sensitive to the atmospheric turbulence and easily distorted. In this paper, an
adaptive compensation method using deep learning technology is developed to improve the performance of
OAM-encoded QKD schemes. A convolutional neural network model is first trained to learn the mapping rela-
tionship of intensity profiles of inputs and the turbulent phase, and such mapping is used as feedback to control a
spatial light modulator to generate a phase screen to correct the distorted vortex beam. Then an OAM-encoded
QKD scheme with the capability of real-time phase correction is designed, in which the compensation module
only needs to extract the intensity distribu tions of the Gaussian probe beam and thus ensures that the information
encoded on OAM states would not be eavesdropped. The results show that our method can efficiently improve the
mode purity of the encoded OAM states and extend the secure distance for the involved QKD protocols in the
free-space channel, which is not limited to any specific QKD protocol.
© 2021 Chinese Laser Press
https://doi.org/10.1364/PRJ.409645
1. INTRODUCTION
Quantum key distribution (QKD) can provide information
theoretic security to share keys between two distant parties
[1–3]. Currently, free-space quantum communication has pro-
gressed out of laboratories into real-world scenarios [4–8],
which paves the way towards global-scale and highly secure
quantum communication networks. However, most experi-
ments mainly rely on either the polarization [9,10] or phase
[11] of faint laser pulses as information carriers, where the
typical two-dimensional encoding scheme limits the capacity
of QKD systems due to an intrinsically bounded Hilbert
space.
Unlike the limited degree of freedom on polarization or
phase states, the orbital angular momentum (OAM) is a
high-dimensional encoding scheme for free-space QKD owing
to an infinite number of available OAM eigenstates in principle.
Recently, Refs. [12–15] implemented OAM-encoded QKD ex-
periments, and Ref. [16] realized OAM-based entanglement
distribution over a free-space optical (FSO) channel of more
than 143 km. Furthermore, OAM has been experimentally
demonstrated to be rotational invariant in the propagation di-
rection, which can remove the error caused by reference frame
misalignment [17]. These outstanding properties make OAM
states useful in both classical communication [18–22] and
high-dimensional quantum cryptography [23–31].
Nonetheless, it has been shown that the helical phase of a
vortex beam that carries OAM is sensitive to the transmission
environment and easily distorted [32–34]. Particularly in a free-
space optical channel, the atmospheric turbulence resulting
from the inhomogeneity of temperature and pressure in the
atmosphere will lead to severe wavefront distortion and coher-
ence destruction of the beam, which will directly increase the
crosstalk among the adjacent OAM modes [35,36] and further
influence the performance of the key rate in OAM-encoded
QKD schemes. Some meaningful methods, such as a post-se-
lection of the data or an increase in the mode spacing, which are
usually used in OAM-encoded QKD systems to improve the
stability of vortex beams against atmospheric turbulence, will
lead to a reduction of single-photon gain and coding dimen-
sion. In addition, an adaptive optics (AO) system is often
Research Article
Vol. 9, No. 2 / February 2021 / Photonics Research B9
2327-9125/21/0200B9-09 Journal © 2021 Chinese Laser Press