PHYSICAL REVIEW A 97, 052328 (2018)
Security analysis of orthogonal-frequency-division-multiplexing–based continuous-variable
quantum key distribution with imperfect modulation
Hang Zhang, Yu Mao, Duan Huang, Jiawei Li, Ling Zhang,
*
and Ying Guo
School of Information Science and Engineering, Central South University, Changsha 410083, China
(Received 18 December 2017; published 29 May 2018)
We introduce a reliable scheme for continuous-variable quantum key distribution (CV-QKD) by using
orthogonal frequency division multiplexing (OFDM). As a spectrally efficient multiplexing technique, OFDM
allows a large number of closely spaced orthogonal subcarrier signals used to carry data on several parallel data
streams or channels. We place emphasis on modulator impairments which would inevitably arise in the OFDM
system and analyze how these impairments affect the OFDM-based CV-QKD system. Moreover, we also evaluate
the security in the asymptotic limit and the Pirandola-Laurenza-Ottaviani-Banchi upper bound. Results indicate
that although the emergence of imperfect modulation would bring about a slight decrease in the secret key bit
rate of each subcarrier, the multiplexing technique combined with CV-QKD results in a desirable improvement
on the total secret key bit rate which can raise the numerical value about an order of magnitude.
DOI: 10.1103/PhysRevA.97.052328
I. INTRODUCTION
Quantum key distribution (QKD), as a major practical
application of quantum information, provides the interaction
for two parties to share a secret key over an unsecure quantum
channel [1–3]. Continuous-variable quantum key distribution
(CV-QKD) offers the prospect of high-detection efficiency and
the tantalizing promise of providing higher key distribution
rates, which are the most highlighted advantages compared
with discrete-variable quantum key distribution (DV-QKD)
protocols [4–6]. The theoretical security of CV-QKD has been
established against general collective Gaussian attacks [7,8],
which have been shown to be optimal in the asymptoti-
cal limit [9]. However, the CV-QKD scheme was initially
plagued with various kinds of problems regarding extending
the secure communication distance and increasing secret key
rates [10,11]. There are two major problems that limit the secret
key rate. The first is the available bandwidth of shot-noise-
limited homodyne detectors and the second is the limited speed
and efficiency of classical reconciliation [12,13]. Recently, a
CV-QKD experiment has been demonstrated over a 25-km
fiber channel with a record secret key rate of 1 Mbps [14]. In
order to increase the secure key rate, an approach is to improve
the currently achievable transport frequencies. However, this
requires faster data acquisition cards, wider bandwidth of
quantum detectors, and a higher speed of postprocessing
procedure, all of which will result in a cumbersome process in
experiments.
In recent years, orthogonal frequency division multiplex-
ing (OFDM) has attracted significant attention in fiberoptic
communications due to its ability to provide higher spectral
efficiency of transmission [15,16]. Many groups have demon-
strated the suitability of OFDM and its variants for long-haul
optical communication systems [17,18]. In this paper, we
*
lingzhang2017@foxmail.com
illustrate and analyze the use of the OFDM technique to
improve the secret key rate and overcome the high-rate issues
in the CV-QKD protocol. In our scheme, a modulated separate
subcarrier after being overlapped by the OFDM system will
form a multiplexing signal. Each individual secret key rate of
its own subcarrier will be calculated independently. Moreover,
the total secret key rate can be added up after homodyne or
heterodyne detection at Bob’s side.
However, the performance of OFDM systems is sensitively
affected by in-phase and quadrature imbalance (I/Q imbal-
ance) of down converter modulators [19]. The I/Q modulators
usually have inevitable imperfections that would result in an
imperfect match between the two baseband analog signals,
I and Q, which represent the complex carrier [20]. In this
paper, we address modulator impairments and discuss how
these impairments affect OFDM-based CV-QKD systems.
At the same time, We conduct the security analysis of
the practical OFDM-based CV-QKD protocol with imper-
fect modulation and illustrate the secret key bit rate in the
asymptotic limit for each subchannel and the whole system.
Further, we review the Pirandola-Laurenza-Ottaviani-Banchi
(PLOB) upper bound of the multiband quantum channel,
and the comprehensive comparisons between the secret key
capacity of OFDM CV-QKD and the PLOB bound scenario are
employed.
This paper is organized as follows. In Sec. II, we mainly
introduce the OFDM-based CV-QKD protocol with imperfect
modulation. In Sec. III, we give the security analysis of the
OFDM CV-QKD protocol with imperfect modulation, and we
give the calculations for the secret key rate. In Sec. IV, the bit
error rates and the secret key rates of the modified protocol and
the original protocol are compared for performance analysis.
The PLOB bound is plotted and discussed as a comparison with
the OFDM CV-QKD scenario. Furthermore, we also illustrate
the impact on the loss ratio of the secret key bit rate versus
the transmission distance under the situation of I/Q imbalance.
Our conclusions are drawn in Sec. V.
2469-9926/2018/97(5)/052328(9) 052328-1 ©2018 American Physical Society