光学源监控：连续变量量子密钥分发的安全保障
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"量子密钥分发的源监控对于连续变量量子密钥分发（CVQKD）的安全性至关重要。文章提出了两种可行的方案，一种基于主动光学开关，另一种基于被动分束器，来监测源噪声的方差。研究了在渐近极限下这两种方案对抗集体攻击的安全界限，并发现被动方案的表现更优。同时，文章还简要讨论了有限尺寸效应对两方案的影响。"
在量子通信领域，尤其是量子密钥分发（QKD）中，源监控是一个关键环节，确保信息传输的安全性。连续变量量子密钥分发是QKD的一种实现方式，利用连续光变量如幅度和相位的量子态进行密钥的交换。相较于基于单光子的离散变量QKD系统，CVQKD通常具有更高的信号检测效率和更快的传输速率，使得它在实际应用中更具潜力。
本研究主要关注CVQKD中光源的噪声问题，因为噪声可能被潜在的窃听者利用，破坏系统的安全性。为了确保安全，文章提出了两种监测源噪声的方法：一是采用主动光学开关方案，二是采用被动分束器方案。主动光学开关方案通过控制开关的开闭，周期性地对光源进行采样，以获取噪声信息。而被动分束器方案则利用分束器将光源随机分为测量和传输两部分，从而无损地监测源噪声。
文章通过理论分析，得出了在无限数据量（渐近极限）情况下，两种方案对抗集体攻击的安全界限。结果显示，被动分束器方案在安全性上优于主动光学开关方案，这可能是由于其更少地干扰了原始的量子态，降低了因操作引入的额外噪声。
此外，作者还考虑了实际应用中的有限数据尺寸效应，即在有限的数据样本下，安全性能会受到何种程度的影响。这部分讨论对于理解实际操作中的CVQKD系统性能至关重要，因为实验中往往难以达到理想的无限数据量条件。
这项工作对于提高CVQKD系统的安全性具有重要的理论与实践意义，提供了源噪声监测的新策略，并对实际系统的设计优化提供了指导。通过比较和分析不同的监测方法，可以更好地理解和改善QKD系统的性能，进一步推动量子通信技术的发展。
PHYSICAL REVIEW A 86, 042314 (2012)
Source monitoring for continuous-variable quantum key distribution
Jian Yang, Bingjie Xu, and Hong Guo
*
State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computer Science,
Peking University, Beijing 100871, People’s Republic of China
(Received 9 July 2012; published 15 October 2012)
The noise in optical source preparation needs to be characterized for the security of practical continuous-variable
quantum key distribution (CVQKD). Two feasible schemes, based on either an active optical switch or a passive
beamsplitter, are proposed to monitor the variance of the source noise. We derive the security bounds for both
schemes against collective attacks in the asymptotical limit and find that the passive scheme performs better. The
finite-size effect is also discussed briefly for both schemes.
DOI: 10.1103/PhysRevA.86.042314 PACS number(s): 03.67.Dd, 03.67.Hk
I. INTRODUCTION
Continuous-variable quantum key distribution (CVQKD)
has developed rapidly in recent years [1,2]. With a high detec-
tion efficiency and repetition rate, it is hopeful that CVQKD,
especially the coherent-stated-based protocol [3,4], will realize
high-speed key generation between two remote parties, Alice
and Bob [5]. Besides experimental demonstrations [6,7], the
theoretical security of CVQKD has also been established
against collective Gaussian attacks [8,9], which has been
shown to be optimal in the asymptotical limit [10].
The practical security of CVQKD has also been noticed in
recent years. It has been shown that the secure key rate may
be undermined by the source noise [11–13]. Taking the GG02
protocol [3], for example, Alice randomly displaces coherent
states following a Gaussian distribution with variance V − 1,
while in practice, due to the imperfections of the optical source
and modulators, the variance of the output state is changed to
V + χ
s
, where χ
s
corresponds to the effect of source noise.
Traditionally, source noise is ascribed into the channel noise to
calculate the secure key rate, while in practice it is controlled
neither by the eavesdropper (Eve), nor by legitimate users.
So, this untrusted source noise model just overestimates Eve’s
power and leads to an untight security bound. To solve this
problem a general source noise model was proposed, where
the source noise is assumed to be introduced by a general
unitary transformation [14]. Without extra assumptions on the
quantum channel and ancilla state, a tight security bound can
be derived for reverse reconciliation, as long as the variance of
the source noise χ
s
can be properly estimated. The optimality
of Gaussian attacks [15,16] is also kept in this scheme [14].
In previous work, the variance of source noise χ
s
was
assumed to have known values, while in practice χ
s
should
be estimated from the experimental data with proper methods.
Without this procedure, Alice and Bob are not able to
discriminate the source noise from the channel excess noise
in the experiment [17], and the previous source noise model
is not able to be implemented in the experiment. In this paper,
we propose two schemes to monitor the variance of the source,
the active switch scheme and the passive beamsplitter scheme,
which can be implemented under current technology. The
security bounds for both schemes are derived against collective
*
Corresponding author: hongguo@pku.edu.cn.
Gaussian attacks in the asymptotical limit and the passive
beamsplitter scheme is found to have a better performance.
Also, we study their potential applications in the real-time
system, in which the finite-size effect should be taken into
account.
II. SOURCE MONITORING IN CVQKD
In this section, we propose two schemes to monitor the
variance of source noise. Both schemes are implemented in
the prepare-and-measure scheme (P&M scheme) [18], while
for the ease of theoretical research we analyze their security in
the equivalent entanglement-based scheme (EB scheme) [19].
The covariance matrix is defined by [18]
γ
ij
= Tr[ ˆρ{(
ˆ
r
i
− d
i
),(
ˆ
r
j
− d
j
)}], (1)
where
ˆ
r
2i−1
=
ˆ
x
i
,
ˆ
r
2i
=
ˆ
p
i
, d
i
=
ˆ
r
i
=Tr[ ˆρ
ˆ
r
i
], ˆρ is the
density matrix, and {} denotes the anticommutator.
In the EB scheme, Alice prepares Einstein-Podolsky-Rosen
(EPR) pairs, measuring the quadratures of one mode with two
balanced homodyne detectors, and then sends the other mode
to Bob. The covariance matrix of an EPR pair is
γ
AB
0
=
V I
√
V
2
− 1σ
z
√
V
2
− 1σ
z
V I
, (2)
where V = V
A
+ 1 is the variance of the EPR modes and
V
A
corresponds to Alice’s modulation variance in the P&M
scheme. However, due to the effect of source noise the actual
covariance matrix is changed to
γ
AB
0
=
V I
√
V
2
− 1σ
z
√
V
2
− 1σ
z
(V + χ
s
)I
, (3)
where χ
s
is the variance of the source noise. The reason
why only mode B
0
is affected can be understood from the
corresponding P&M scheme in which Alice prepares the
coherent state |Q
A
+ iP
A
and sends it to Bob, where Q
A
and P
A
follow Gaussian distribution with variances (V − 1).
Due to the effect of source noise, the actual state sent to
Bob is |(Q
A
+ δQ
A
) + i(P
A
+ δP
A
), where δQ
A
and δP
A
are introduced by the source noise and also follow Gaussian
distribution with variances χ
s
. In this case, it is not difficult
to verify the corresponding covariance matrix γ
AB
0
accords
with Eq. (3) [14,17]. As mentioned by the authors of [14],
we assume this noise is introduced by a neutral party, Fred,
042314-1
1050-2947/2012/86(4)/042314(6) ©2012 American Physical Society
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