MDI QKD的有限密钥分析：去中心化量子密钥的实践挑战

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在现实的量子密钥分发(QKD)系统中，信号脉冲的长度是有限的，这是一个实际操作中不可忽视的重要因素。传统的无限密钥分析假设在理论上是理想的，但在实际应用中，这种理想化的处理方式无法涵盖信号长度受限带来的影响。因此，对无条件量子密钥分发的有限键分析（finite-key analysis）成为一个亟待解决的关键问题。近期，一种旨在克服实际限制、提高效率的量子密钥分发协议——测量设备独立量子密钥分发（MDI QKD）被提出。MDI QKD通过消除所有检测器侧信道，显著提升了安全性和实用性。它的核心原理在于，它不依赖于任何特定的测量设备，这在很大程度上保护了系统的安全性，即使在存在潜在漏洞的设备中也能确保密钥的安全传输。这篇发表在《物理评论A》(Physical Review A)第86卷第2期的研究论文，作者Ting-Ting Song、Qiao-Yan Wen、Fen-Zhuo Guo 和 Xiao-Qing Tan，探讨了MDI QKD的有限键分析方法。他们考虑了实际信号脉冲长度有限情况下，如何对密钥生成率进行准确估计，以及如何在有限数据集下保持协议的有效性和安全性。研究的核心内容包括对MDI QKD的安全性界限进行量化，这涉及到计算在有限的实验数据集下，误码率、量子比特错误率和信息泄露率等关键参数。他们采用统计方法，如二项分布和Hoeffding's inequality等，来评估在有限样本量下这些参数的可信区间，从而给出一个实际可行的密钥生成速率，并确保安全性的保守估计。此外，论文还探讨了如何优化MDI QKD的实现，例如通过选择合适的信号和态的参数配置，以最大化在有限键长度下的性能。这可能涉及到对密钥分发速率与实验复杂度之间的权衡，以及如何在实际部署中考虑到噪声、设备损耗等因素。这篇论文为MDI QKD的实用化提供了重要的理论支持，特别是在面对信号脉冲长度有限这一实际挑战时，它为量子密钥分发协议设计者和实施者提供了一套完整的有限键分析框架，以确保在实际环境中的高效和安全运行。

PHYSICAL REVIEW A 86, 022332 (2012)

Finite-key analysis for measurement-device-independent quantum key distribution

Ting-Ting Song,

1,2,*

Qiao-Yan Wen,

Fen-Zhuo Guo,

and Xiao-Qing Tan

State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China

Center for Quantum Information and Quantum Control, Department of Electrical and Computer Engineering and Department of Physics,

University of Toronto, Toronto, Ontario, Canada M5S 3G4

Department of Mathematics, College of Information Science and Technology, Jinan University, Guangzhou, Guangdong 510632, China

(Received 25 April 2012; published 27 August 2012)

The length of signal pulses is ﬁnite in practical quantum key distribution. The ﬁnite-key analysis of an

unconditional quantum key distribution is a burning problem, and the efﬁcient quantum key distribution protocol

suitable for practical implementation, measurement-device-independent quantum key distribution (MDI QKD),

was proposed very recently. We give the ﬁnite-key analysis of MDI QKD, which removes all detector side channels

and generates many orders of key rate higher than that of full-device-independent quantum key distribution. The

secure bound of the ultimate key rate is obtained under the statistical ﬂuctuations of relative frequency, which

can be applied directly to practical threshold detectors with low detection efﬁciency and highly lossy channels.

The bound is evaluated for reasonable values of the observed parameters. The simulation shows that the secure

distance is around 10 km when the number of sifted data is 10

. Moreover the secure distance would be much

longer in practice because of some simpliﬁed treatments used in our paper.

DOI: 10.1103/PhysRevA.86.022332 PACS number(s): 03.67.Dd

I. INTRODUCTION

In 1984, Bennett and Brassard proposed the ﬁrst quantum

key distribution (QKD) protocol, known as BB84 [1]. In this

protocol, two parties, Alice and Bob, can generate a secure

key string in the presence of an eavesdropper, Eve [2,3]. The

research interest in QKD then grew quickly [4,5]. In 1996,

Mayers [6] introduced the ﬁnite-key analysis of QKD; i.e.,

the number of pulses sent by the communication parties is

ﬁnite. Then he, cooperating with Inamori and L

utkenhaus [7],

analyzed the security of QKD in a realistic setup (highly lossy

channel and non-single-photon source) after Hwang [8]gave

the security analysis of the standard BB84 protocol based on a

non-single-photon source by decoy method. However, K

onig

et al. [9] showed that in the previous ﬁnite-key security of the

standard BB84 protocol, some potential problems exist with

respect to the difference between the two information entropies

(Alice and Bob versus Alice and Eve). They then proposed a

universal composable security deﬁnition. The new deﬁnition

indicates that the security can be judged by the distance

between the ultimate secret key and the perfect key which

is uniformly distributed and completely independent from the

eavesdropper’s quantum system. According to this modiﬁed

deﬁnition of security, Cai and Scarani [10] analyzed the

simpliﬁed ﬁnite-key security of the standard BB84 protocol,

while some other researchers [11–13] gave the upper bounds

of eavesdropper’s information entropy on a secret key and the

ﬁnite-key analysis under collective attack.

However, there still exists a gap between theory and

experiment. Quantum hackers have exploited security loop-

holes in real-life quantum systems. Various attacks have been

successfully launched against commercial QKD systems, for

instance, time-shift attacks [14], phase remapping attacks [15],

blinding attacks [16], and wavelength-dependent attacks [17].

One effective approach that can resist these attacks is device-

tingting.song.china@gmail.com

independent QKD (DI QKD). It is called device independent

because the protocol does not need any assumptions about

the internal workings of the quantum settings used in the

protocol and only demands those eavesdroppers must obey

the laws of quantum physics, the choice of measurement basis

is free, and there is no leakage of information from Alice’s

and Bob’s laboratories. The security of DI QKD [18–21]is

based on the ﬁdelity of Einstein-Podolsky-Rosen (EPR) pairs

sent to two parties from an untrusted relay source, which

can be detected by Clauser-Horne-Shimony-Holt (CHSH)

measurements. Unfortunately, the secure key rate of DI QKD

is small, on the order of 10

−10

, and the transmitted distance is

around 5 km, with a lossy quantum channel. An effective

method that can enlarge the secure distance needs to be

established.

Recently, an approach called measurement-device-

independent QKD (MDI QKD) has been proposed [22]. The

key rate of MDI QKD is many orders of magnitude higher than

that of DI QKD. In this scheme, the communication parties,

say Alice and Bob, do not need to do any measurement; they

only need to prepare the pulses and send them to an untrusted

relay who is placed between Alice and Bob and who operates

the measurement. Then, with an announcement from the relay

about successful outcomes, Alice and Bob sift the data they

hold and perform the standard classical postprocessing on the

sifted data, such as error correction and privacy ampliﬁcation.

Then they obtain the secure key string. This MDI QKD

protocol does not put any assumptions on the measurement

device, so it can remove the side-channel attack occurring in

detectors, which is more dominant than side attacks operated

in other devices. In contrast to standard DI QKD, MDI QKD

focuses on the signal source and assumes that Alice and Bob

have almost perfect state preparation. Currently, attenuated

laser pulses are used as practical sources, especially for the

weak coherent source. And the security of MDI QKD based

on the weak coherent source has been veriﬁed. However, for

the application of MDI QKD in practice, another weakness,

the asymptotic resource of optical pulses, is assumed, which

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