Security of continuous-variable measurement-device-independent quantum key distribution with imperfect state preparation

The state preparation operation of continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol may become imperfect in practical applications. We address the security of the CV-MDI-QKD protocol based on imperfect preparation of the coherent state under realistic conditions of lossy and noisy quantum channel. Specifically, we assume that the imperfection of Alice's and Bob's practical state preparations equal to the amplification of ideal modulators and lasers at both Alice's and Bob's sides by untrusted third-parties Fred and Gray employing phase-insensitive amplifiers (PIAs), respectively. The equivalent excess noise introduced by the imperfect state preparation is comprehensively and quantitatively calculated by adopting the gains of PIAs. Security analysis shows that CV-MDI-QKD is quite sensitive to the imperfection of practical state preparation, which inevitably deteriorates the performance and security of CV-MDI-QKD system. Moreover, a lower bound of the secret key rate is derived under arbitrary collective attacks, and the upper threshold of this imperfection tolerated by the system is obtained in the form of the specific gains of PIAs. In addition, the methods presented will improve and perfect the practical security of CV-MDI-QKD protocol.     

Improvement of a continuous-variable measurement-device-independent quantum key distribution system via quantum scissors

We propose a new scheme to enhance the performance of the Gussian-modulated coherent-state continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) system via quantum scissors (QS) operation at Bob's side. As an non-deterministic amplifying setup, we firstly introduce the QS-enhanced CV-MDI-QKD protocol and then investigate the success probability of the QS operation in accordance with the equivalent one-way scheme. Afterwards, we investigate the effect of the QS operation on the proposed scheme and analyze the performance of the QS-enhanced CV-MDI-QKD system under the extreme asymmetric circumstance. Simulation results show that the QS operation can indeed improve the performance of the CV-MDI-QKD system considerably. QS-enhanced CV-MDI-QKD protocol outperforms the original CV-MDI-QKD protocol in both the maximum transmission distance and the secret key rate. Moreover, the better the performance of QS operation, the more significant the improvement of performance of the system.     

Improving the Performance of Continuous-Variable Measurement-Device-Independent Quantum Key Distribution via a Noiseless Linear Amplifier

In the continuous variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol, both Alice and Bob send quantum states to an untrusted third party, Charlie, for detection through the quantum channel. In this paper, we mainly study the performance of the CV-MDI-QKD system using the noiseless linear amplifier (NLA). The NLA is added to the output of the detector at Charlie’s side. The research results show that NLA can increase the communication distance and secret key rate of the CV-MDI-QKD protocol. Moreover, we find that the more powerful the improvement of the performance with the longer gain of NLA and the optimum gain is given under different conditions.     

Measurement-device-independent quantum secure direct communication

Quantum secure direct communication(QSDC)is a unique technique,which supports the secure transmission of confidential information directly through a quantum channel without the need for a secret key and for ciphertext.Hence this secure communication protocol fundamentally differs from its conventional counterparts.In this article,we report the first measurement-deviceindependent(MDI)QSDC protocol relying on sequences of entangled photon pairs and single photons.Explicitly,it eliminates the security loopholes associated with the measurement device.Additionally,this MDI technique is capable of doubling the communication distance of its conventional counterpart operating without using our MDI technique.We also conceive a protocol associated with linear optical Bell-basis measurements,where only two of the four Bell-basis states could be measured.When the number of qubits in a sequence reduces to 1,the MDI-QSDC protocol degenerates to a deterministic MDI quantum key distribution protocol.     

离散调制连续变量量子密钥分发的安全边界

对一种结合离散调制和反向协调,适用于长距离传输的连续变量量子密钥分发四态协议的安全性进行了严格证明.这种协议中Alice发送的态与高斯调制协议中的有一定差异,这种差异可以等价成信道衰减和额外噪声.另外,由于Alice不可能做到精确调制,这会导致其发送的相干态中含有噪声.把这种调制引起的噪声看作光源的噪声,并推导出了在光源噪声不能被窃听者所利用的条件下的安全码率的下界.为了避免实验上快速、随机的控制本地振荡光的相位,还将无开关协议和四态协议相结合,分析了其安全性.     

Nuclear compression moduli and density-dependent forces

Density-dependent zero-range forces of the form of the modified delta interaction (MDI) are generalized (MDI3, MDI4) in order to yield reasonable values of the compression modulus in nuclear matter (K_N = 200 MeV). This low value can be fitted by introducing two terms with different density dependence in the force. The four free parameters of MDI3 are adjusted to reproduce the nuclear matter values of the binding energy, density and compression modulus, and to fulfil the condition that the total energy of ¹⁶O in harmonic oscillator wave functions has a minimum at the oscillator length b = 1.75 fm, corresponding to the correct rms radius. MDI4 contains in addition a two-body spin-orbit interaction. The five parameters of MDI4 are fitted to the above three nuclear matter data and by requiring that Hartree-Fock (HF) calculations in ²⁰⁸Pb yield the experimental charge rms radius and reasonable values of certain single-particle spin-orbit splittings. The quality of MDI4 is checked by comparing calculated rms radii, binding energies, and elastic electron scattering cross sections with available experimental data for doubly closed shell nuclei. As a test the energy levels and the nuclear monopole polarization of muonic ²⁰⁸Pb are calculated self-consistently yielding impressive agreement with experiment.     

Energy levels of one-dimensional systems satisfying the minimal length uncertainty relation

The standard approach to calculating the energy levels for quantum systems satisfying the minimal length uncertainty relation is to solve an eigenvalue problem involving a fourth- or higher-order differential equation in quasiposition space. It is shown that the problem can be reformulated so that the energy levels of these systems can be obtained by solving only a second-order quasiposition eigenvalue equation. Through this formulation the energy levels are calculated for the following potentials: particle in a box, harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well. For the particle in a box, the second-order quasiposition eigenvalue equation is a second-order differential equation with constant coefficients. For the harmonic oscillator, Pöschl–Teller well, Gaussian well, and double-Gaussian well, a method that involves using Wronskians has been used to solve the second-order quasiposition eigenvalue equation. It is observed for all of these quantum systems that the introduction of a nonzero minimal length uncertainty induces a positive shift in the energy levels. It is shown that the calculation of energy levels in systems satisfying the minimal length uncertainty relation is not limited to a small number of problems like particle in a box and the harmonic oscillator but can be extended to a wider class of problems involving potentials such as the Pöschl–Teller and Gaussian wells.     

Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

This paper aims to investigate the stochastic response of the van der Pol(VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation.First,the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique.Then,the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution.Finally,the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator.The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order,the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator.An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary.     

Performance analysis of continuous-variable measurement-device-independent quantum key distribution under diverse weather conditions

The effects of weather conditions are ubiquitous in practical wireless quantum communication links.Here in this work,the performances of atmospheric continuous-variable measurement-device-independent quantum key distribution(CV-MDI-QKD) under diverse weather conditions are analyzed quantitatively.According to the Mie scattering theory and atmospheric CV-MDI-QKD model,we numerically simulate the relationship between performance of CV-MDI-QKD and the rainy and foggy conditions,aiming to get close to the actual combat environment in the future.The results show that both rain and fog will degrade the performance of the CV-MDI-QKD protocol.Under the rainy condition,the larger the raindrop diameter,the more obvious the extinction effect is and the lower the secret key rate accordingly.In addition,we find that the secret key rate decreases with the increase of spot deflection distance and the fluctuation of deflection.Under the foggy condition,the results illustrate that the transmittance decreases with the increase of droplet radius or deflection distance,which eventually yields the decrease in the secret key rate.Besides,in both weather conditions,the increase of transmission distance also leads the secret key rate to deteriorate.Our work can provide a foundation for evaluating the performance evaluation and successfully implementing the atmospheric CV-MDI-QKD in the future field operation environment under different weather conditions.     

Quantum Private Comparison of Equality with χ-Type Entangled States

In this paper, a quantum private comparison protocol with χ-type entangled states is proposed. In the protocol, two users can determine whether their secret inputs are equal, with the help of a semi-trusted third party. Here, the only constraint condition of this third party is that he could not collude with one user. Although the third party takes part in the whole process of the presented protocol, a feature of χ-type entangled state is utilized to design a eavesdropping check method to stand against his attack. Security analysis showed that the presented protocol is secure against some well-known attacks. Meanwhile, all the particles undergo only a one-way trip, which improves the efficiency and security of the presented protocol. Furthermore, only two-particle measurement is required in the implementation of the protocol, which make it more feasible in technique.     

Security Analysis of Measurement-Device-Independent Quantum Key Distribution in Collective-Rotation Noisy Environment

Noise is a problem that communication channels cannot avoid. It is, thus, beneficial to analyze the security of MDI-QKD in noisy environment. An analysis model for collective-rotation noise is introduced, and the information theory methods are used to analyze the security of the protocol. The maximum amount of information that Eve can eavesdrop is 50%, and the eavesdropping can always be detected if the noise level ε ≤ 0.68. Therefore, MDI-QKD protocol is secure as quantum key distribution protocol. The maximum probability that the relay outputs successful results is 16% when existing eavesdropping. Moreover, the probability that the relay outputs successful results when existing eavesdropping is higher than the situation without eavesdropping. The paper validates that MDI-QKD protocol has better robustness.     

Splitting algorithm for DMT optimal cooperative MAC protocols in wireless mesh networks

A cooperative protocol for wireless mesh networks is proposed in this paper. The protocol implements both on-demand relaying and a selection of the best relay terminal so only one terminal is relaying the source message when cooperation is needed. Two additional features are also proposed. The best relay is selected with a splitting algorithm. This approach allows fast relay selection within less than three time-slots, on average. Moreover, a pre-selection of relay candidates is performed prior to the splitting algorithm. Only terminals that are able to improve the direct path are pre-selected. So efficient cooperation is now guaranteed. We prove that this approach is optimal in terms of diversity-multiplexing trade-off. The protocol has been designed in the context of Nakagami-m fading channels. Simulation results show that the performance of the splitting algorithm does not depend on channel statistics.     

Plug-and-play dual-phase-modulated continuous-variable quantum key distribution with photon subtraction

Plug-and-play dual-phase-modulated continuous-variable quantum key distribution (CVQKD) protocol can effectively solve the security loopholes associated with transmitting local oscillator (LO). However, this protocol has larger excess noise compared with one-way Gaussian-modulated coherent-states scheme, which limits the maximal transmission distance to a certain degree. In this paper, we show a reliable solution for this problem by employing non-Gaussian operation, especially, photon subtraction operation, which provides a way to improve the performance of plug-and-play dual-phase-modulated CVQKD protocol. The photon subtraction operation shows experimental feasibility in the plug-andplay configuration since it can be implemented under current technology. Security results indicate that the photon subtraction operation can evidently enhance the maximal transmission distance of the plug-and-play dual-phase-modulated CVQKD protocol, which effectively makes up the drawback of the original one. Furthermore, we achieve the tighter bound of the transmission distance by considering the finite-size effect, which is more practical compared with that achieved in the asymptotic limit.     

Secure Polar Coding for the Primitive Relay Wiretap Channel

With the emergence of wireless networks, cooperation for secrecy is recognized as an attractive way to establish secure communications. Departing from cryptographic techniques, secrecy can be provided by exploiting the wireless channel characteristics; that is, some error-correcting codes besides reliability have been shown to achieve information-theoretic security. In this paper, we propose a polar-coding-based technique for the primitive relay wiretap channel and show that this technique is suitable to provide information-theoretic security. Specifically, we integrate at the relay an additional functionality, which allows it to smartly decide whether it will cooperate or not based on the decoding detector result. In the case of cooperation, the relay operates in a decode-and-forward mode and assists the communication by transmitting a complementary message to the destination in order to correctly decode the initial source’s message. Otherwise, the communication is completed with direct transmission from source to the destination. Finally, we first prove that the proposed encoding scheme achieves weak secrecy, then, in order to overcome the obstacle of misaligned bits, we implement a double-chaining construction, which achieves strong secrecy.     

The queuing delay analysis at relay node based on cooperative GBN-ARQ protocols

In this paper, a single relay cooperative diversity network model is proposed, analyzing queuing delay of the packets at relay node. Using dynamic radio link adaptation in wireless networks, based on the character of GBN-ARQ protocol and the queuing theory, the paper solves the problem that packets wait to transmit at relay, and presents a relay node to destination node queuing analysis model for GBN-ARQ protocol with fixed feedback delay. The paper establishes Markov model of packet transmission, and the delay statistics at relay node are figured out by using matrix geometric methods.     

基于旋转不变态的测量设备无关量子密钥分配协议研究

本文提出了一种基于旋转不变态的偏振无关测量设备量子密钥分配协议,既适用于偏振编码测量设备无关量子密钥分配系统,也应用于相位编码测量设备无关量子密钥分配系统的相干过程.通过在线偏振基进入信道传输前嵌入2块q玻片,使得在传输过程中将线偏振基转化为旋转不变的圆偏振基,而第三方对接收到的脉冲进行Bell态测量前,利用q玻片的算符可逆性,将圆偏振基还原为线偏振基进行测量,可以有效消除信道传输中偏振旋转导致的误码.本文分析了偏振无关的三诱骗态测量设备无关量子密钥分配系统的误码率,研究了密钥生成率与安全传输距离的关系,仿真结果表明,对于偏振编码测量设备无关量子密钥分配系统,该协议可以有效提高系统的最大安全通信距离,为实用的量子密钥分配实验提供了重要的理论参数.     

Continuous-variable Measurement-device-independent Quantum Relay Network with Phase-sensitive Amplifiers

Continuous-variable (CV) measurement-device-independent (MDI) quantum cryptography is now heading towards solving the practical problem of implementing scalable quantum networks. In this paper, we show that a solution can come from deploying an optical amplifier in the CV-MDI system, aiming to establish a high-rate quantum network. We suggest an improved CV-MDI protocol using the EPR states coupled with optical amplifiers. It can implement a practical quantum network scheme, where the legal participants create the secret correlations by using EPR states connecting to an untrusted relay via insecure links and applying the multi-entangled Greenberger-Horne-Zeilinger (GHZ) state analysis at relay station. Despite the possibility that the relay could be completely tampered with and imperfect links are subject to the powerful attacks, the legal participants are still able to extract a secret key from network communication. The numerical simulation indicates that the quantum network communication can be achieved in an asymmetric scenario, fulfilling the demands of a practical quantum network. Furthermore, we show that the use of optical amplifiers can compensate the inherent imperfections and improve the secret key rate of the CV-MDI system.     

Self-referenced continuous-variable measurement-device-independent quantum key distribution

We propose a scheme to remove the demand of transmitting a high-brightness local oscillator (LO) in continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, which we call as the self-referenced (SR) CV-MDI QKD. We show that our scheme is immune to the side-channel attacks, such as the calibration attacks, the wavelength attacks and the LO fluctuation attacks, which are all exploiting the security loopholes introduced by transmitting the LO. Besides, the proposed scheme waives the necessity of complex multiplexer and demultiplexer, which can greatly simplify the QKD processes and improve the transmission efficiency. The numerical simulations under collective attacks show that all the improvements brought about by our scheme are only at the expense of slight transmission distance shortening. This scheme shows an available method to mend the security loopholes incurred by transmitting LO in CV-MDI QKD.     

Quantum private query: A new kind of practical quantum cryptographic protocol

This research aims to review the developments in the field of quantum private query(QPQ), a type of practical quantum cryptographic protocol. The primary protocol, as proposed by Jacobi et al., and the improvements in the protocol are introduced.Then, the advancements made in sability, theoretical security, and practical security are summarized. Additionally, we describe two new results concerning QPQ security. We emphasize that a procedure to detect outside adversaries is necessary for QPQ, as well as for other quantum secure computation protocols, and then briefly propose such a strategy. Furthermore, we show that the shift-and-addition or low-shift-and-addition technique can be used to obtain a secure real-world implementation of QPQ, where a weak coherent source is used instead of an ideal single-photon source.     

Fiber chromatic dispersion measurement by using a novel RF spectrum phase detection method based on DSP

In this paper, a novel chromatic dispersion (CD) measuring method based on a novel RF spectrum phase detection technique is proposed, this is performed using in-band tone monitoring RF, electrically down-converted to direct current (DC) or a low intermediate-frequency (IF) of less than 1 MHz through electronic mixing with local oscillator (LO). We theoretically and experimentally demonstrated the CD measurement for CD components (etc. fiber). The method can support any CD range measuring with good accuracy through adjusting RF frequency.