Order statistics and random matrix theory of multicarrier continuous‐variable quantum key distribution

In a multicarrier continuous‐variable quantum key distribution (CVQKD) protocol, the information is granulated into Gaussian subcarrier CVs and the physical Gaussian link is divided into Gaussian sub‐channels. Here, we propose a combined mathematical framework of order statistics and random matrix theory for multicarrier continuous‐variable quantum key distribution. The analysis covers the study of the distribution of the sub‐channel transmittance coefficients in the presence of a Gaussian noise and the utilization of the moment generation function (MGF) in the error analysis. We reveal the mathematical formalism of sub‐channel selection and formulation of the transmittance coefficients and show a reduced complexity progressive sub‐channel scanning method. We define a framework to evaluate the statistical properties of the information flowing processes in multicarrier CVQKD protocols. Using random matrix theory, we express the achievable secret key rates and study the efficiency of the adaptive multicarrier quadrature division‐multiuser quadrature allocation (AMQD‐MQA) multiple‐access multicarrier CVQKD. The proposed combined framework is particularly convenient for the characterization of the physical processes of experimental multicarrier CVQKD.     

Diversity space of multicarrier continuous‐variable quantum key distribution

The diversity space of multicarrier continuous‐variable quantum key distribution (CVQKD) is defined. The diversity space utilizes the resources that are injected into the transmission by the additional degrees of freedom of the multicarrier modulation. We prove that the exploitable extra degree of freedom in a multicarrier CVQKD scenario significantly extends the possibilities of single‐carrier CVQKD. The manifold extraction allows for the parties to reach decreased error probabilities by utilizing those extra resources of a multicarrier transmission that are not available in a single‐carrier CVQKD setting. We define the multidimensional manifold space of multicarrier CVQKD and the optimal tradeoff between the available degrees of freedom of the multicarrier transmission. We extend the manifold extraction for the multiple‐access AMQD‐MQA (multiuser quadrature allocation) multicarrier protocol. The additional resources of multicarrier CVQKD allow the achievement of significant performance improvements that are particularly crucial in an experimental scenario.     

Secret key rate proof of multicarrier continuous‐variable quantum key distribution

We prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous‐variable quantum key distribution CVQKD. In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier continuous variables (CVs). The multicarrier communication formulates Gaussian subchannels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single‐carrier Gaussian CVs. We derive the formulas through the adaptive multicarrier quadrature division (AMQD) scheme, the singular value decomposition (SVD)–assisted AMQD, and the multiuser AMQD multiuser quadrature allocation (MQA). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison with single‐carrier CVQKD. We derive the private classical capacity of a Gaussian subchannel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one‐way and two‐way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds.     

中间纠缠源离散调制CVQKD性能分析

连续变量量子密钥分发协议虽然具备更高的安全码 率等优势,但是其安全传输距离却一直表现不佳,而离散调制连续变量量子密钥分发协议已 被证明在低信噪比下能够获得比高斯调制更好的性能。基于 此,本文详细分析了光源非可信时,离散调制二态、四态和八态协议的性能,推导了安全码 率表达式。数 值仿真结果表明,当光源处于中间时,离散调制相干态零差检测正向协调性能优于其它协议 ,八态协议有更长的传输距离。     

自由空间量子密码通信中量子密钥比特率研究

通过引入量子信道传输率、单光子捕获概率、检测因子和数据筛选因子,给出了自由空间量子密钥分配中量子密钥比特率的表达式.针对低轨卫星-地面站间激光链路,进行了量子密钥比特率的数值仿真研究.结果表明,在低轨卫星-地面站间进行量子密钥分配是可行的.     

Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

多用户网络环境下量子密码术

在传统的点到点之间进行量子密钥分发协议的基础上,利用量子存储技术和EPR粒子纠缠态互换的方法,提出了在多用户、多控制中心、远距离的网络环境下进行量子密钥传送的方案。与传统的点与点之间的量子密钥传送协议类似,其安全性也是建立在量子力学原理上,任何窃听者的存在必将使生成密钥的误码率上升而被合法通信用户发现。     

Network‐coded multiple‐source cooperation aided relaying for free‐space optical transmission

A network‐coded cooperative relaying aided free‐space optical (FSO) transmission scheme is designed. The resultant multiple‐source cooperation diversity is exploited by the relay to mitigate the strong turbulence‐induced fading experienced in FSO channels. At the destination, an iterative multiple source detection algorithm is proposed in conjunction with a chip‐level soft network decoding method. Our performance evaluation results using simulation analysis demonstrate that the proposed FSO multiple source detection is capable of approaching the single‐user‐bound for transmission over Gamma–Gamma turbulence channels. Also, the network‐coded cooperative FSO scheme can achieve a significant BER improvement in comparison with conventional noncooperation schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

融合量子密钥分配的电信运营商密码应用体系

基于量子密钥分配（quantum key distribution,QKD）的通信网络具备实现“perfect secrecy”（完美保密性）的能力，当前还不能满足大规模应用的需求，在实际应用中需要结合经典密码技术。提出了融合量子密钥分配的电信运营商密码应用体系的功能架构模型，介绍了模型的层次结构、核心的网元和功能模块以及接口关系，给出了应用体系的整体框架，介绍了框架的主要组成部分，描述了应用体系的典型应用场景及其工作流程。     

基于朴素贝叶斯分类的相位编码连续变量量子密钥分发方案

针对相位编码连续变量量子密钥分发(continous variable quantum key distribution,CVQKD) 在远距离传输时,量子态在接收端的检测效率较低的问题,本文提出在接收端使用朴素贝叶斯(native Bayes,NB)分类器来改进系统性能。NB分类器首先对已标记类别的量子态进行训练,学习不同类别量子态的分布情况,计算每个类别的先验概率和似然概率,再基于先验概率和似然概率计算出待测量子态属于每个类别的后验概率,根据后验概率的大小来确定待测量子态的类别。仿真结果表 明,改进方案可以通过降低测试态在接收端被错误测量的概率来提升系统性能,当过量噪声为0.01时,改进方案的安全距离可以突破250 km。     

安全稳定实用的差分量子密钥分配实验研究

在差分密钥分配通信系统中,嵌入时分复用单光子探测装置,在每次量子密钥分配的同时计量发信者(Alice)用于密钥分配的单脉冲平均光子数,确保通信的安全程度.实现了90 km的稳定的量子保密通信,误码率约为4%,有很好的实用价值.     

量子密码系统中常用量子信号的产生方法

量子密钥分配是量子密码学最成功的应用.如何产生高效的量子信号,是量子密钥分配系统安全运行的关键.文中简要介绍了量子信号的概念,给出了几种产生量子信号的常用方法,并简要分析了这些信号应用于量子密钥分配的可行性.     

MaTRU‐KE revisited: CCA2‐secure key establishment protocol based on MaTRU

Quantum attack–resistant cryptosystems are required for secure communication since there is a big demand to have quantum computers. Lattice‐based cryptography is one of the quantum‐secure families due to its key/ciphertext sizes and performance. NTRU‐based cryptosystems, a member of lattice‐based cryptosystems, have received much more attention. MaTRU, a noncommutative version of NTRU with some matrix properties, is used to obtain a key exchange protocol in 2018. In this paper, we focus on MaTRU‐based key exchange protocols having CCA2 properties. We propose CCA2‐secure versions of MaTRU‐KE and then provide a security analysis of CCA2‐secure key establishment protocols. We also provide a comparison with the previous ones.     

Enhancing spectral efficiency of FSO system using adaptive SIM/M‐PSK and SIMO in the presence of atmospheric turbulence and pointing errors

This paper proposes an adaptive transmission modulation (ATM) technique for free‐space optical (FSO) links over gamma‐gamma turbulence channels.The ATM technique provides efficient utilization of the FSO channel capacity for improving spectral efficiency, by adapting the order of the phase‐shift keying modulation scheme, according to the channel conditions and the required bit error rate (BER). To overcome the channel degradation resulting from the turbulence effects as well as the pointing errors (PEs), single‐input multiple‐output (SIMO) system with maximal ratio combining (MRC) is proposed. Exact closed‐form expressions of BER and upper bound of the capacity are derived and verified by Monte Carlo simulations. The numerical results show that the proposed adaptive technique improves the spectral efficiency (SE) five times higher than the nonadaptive technique at the same BER threshold (10^?3).This improvement is achieved at signal‐to‐noise ratio (SNR) equals 27 and 42  dB in the case of atmospheric turbulence without and with PE, respectively. Furthermore, this SE could be obtained while the SNR = 30  dB by using ( 1 × 4 ) SIMO scheme with MRC and PE and having the same transmitting optical power.     

量子保密通信及其进展

综述了国内外最近在量子密码学研究中的相关研究以及向实用化转化的实验结果,并针对量子密钥分发方案提出了一种改进方案。最后对量子密码体制进行了展望。     

量子密码学的应用研究

文中首先对量子密码学作了简单的介绍,给出了量子密钥所涉及的几个主要量子效应,接着较为详细地阐述了国内外量子密码学发展的历史,给出了量子密码学研究的几个课题：量子密钥分配、量子签名、量子身份认证、量子加密算法、量子秘密共享等,并分别加以简单的说明并详细地分析了阻碍量子密码实用化的几个因素。最后对量子密码学的发展做了展望。     

具有可证明安全性的量子加密算法

加密算法的安全性是保证信息机密性、完整性和可用性的基础。与经典的加密算法不同，量子加密算法具有完全可证明的安全性。本文介绍量子密钥分配协议模型，并针对存在概率克隆机的理论，证明了基于不可克隆原理的量子密钥分配协议具有足够的安全性。     

只用两个量子态的星型量子密钥网络方案

要建立一个安全的保密通信通道,关键就是密钥管理。传统的密钥管理并不能完全解决安全问题,量子密码技术却可以从根本上解决这个问题。本文从实用的角度提出一个基于无源光学网络环境中建立量子密钥的实用方案,这个方法可以由一个网络控制者在一个星型网络上和多个网络用户分别建立、更新密钥。为节约量子探测设备,和通常用四个量子态的保密通信方案相比,这个方案只用了两个量子态。本文还分析了在网络的各个位置上存在窃听时网络的安全性能。     

Atom‐by‐Atom Fabrication of Single and Few Dopant Quantum Devices

Atomically precise fabrication has an important role to play in developing atom‐based electronic devices for use in quantum information processing, quantum materials research, and quantum sensing. Atom‐by‐atom fabrication has the potential to enable precise control over tunnel coupling, exchange coupling, on‐site charging energies, and other key properties of basic devices needed for solid‐state quantum computing and analog quantum simulation. Using hydrogen‐based scanning probe lithography, individual dopant atoms are deterministically placed relative to atomically aligned contacts and gates to build single electron transistors, single atom transistors, and gate‐controlled quantum sensing devices. The key steps required to fabricate and demonstrate the essential building blocks needed for spin selective initialization/readout and coherent quantum manipulation are described.     

基于任意BELL态的量子密钥分配

为了提高量子密钥分配的安全性和效率,利用量子纠缠交换的规律,提出了基于纠缠交换的量子密钥分配协议。通信双方通过简单的BELL测量建立起共享密钥,窃听者不可能窃取密钥而不被发现。该协议与其它分配协议的不同在于,可以实现对任意两个BELL态进行BELL测量达到量子密钥分配的目的。协议的实现只需要EPR粒子对,而不需要制备多粒子纠缠态。分析结果表明,此协议只用到两粒子的纠缠态,不需要进行幺正操作,它不仅能够保证密钥分配的安全性,而且简单高效。