Performance improvement of unidimensional continuous-variable quantum key distribution using heralded hybrid linear amplifier

We propose an improved scheme for unidimensional continuous-variable quantum key distribution (UCVQKD) using heralded hybrid linear amplifier, aiming to simplify the implementation and improve secret key rate. Different from the symmetrical continuous-variable quantum key distribution protocol (CVQKD), this scheme modulates one quadrature of the coherent state with security insurance. The heralded hybrid linear amplifier concatenates a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), which can tune between the high-gain or high noise-reduction for performance enhancement. Security analysis shows that the proposed scheme can be secured under the collective attacks. Compared with traditional UCVQKD involving noiseless amplifier, the security transmission distance of proposed protocol is increased by 24 kilometers. It not only simplifies the modulation process but also has approximate performance with symmetrical CVQKD in terms of maximal security transmission distance.     

Continuous-Variable Quantum Key Distribution Based on Heralded Hybrid Linear Amplifier with a Local Local Oscillator

An improved continuous variable quantum key distribution (CVQKD) approach based on a heralded hybrid linear amplifier (HLA) is proposed in this study, which includes an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The CVQKD, which is based on an amplifier, enhances the signal-to-noise ratio and provides for fine control between high gain and strong noise reduction. We focus on the impact of two types of optical amplifiers on system performance: phase sensitive amplifiers (PSA) and phase insensitive amplifiers (PIA). The results indicate that employing amplifiers, local local oscillation-based CVQKD systems can enhance key rates and communication distances. In addition, the PIA-based CVQKD system has a broader application than the PSA-based system.     

High-Rate Continuous-Variable Quantum Key Distribution with Orbital Angular Momentum Multiplexing

The secret key rate is one of the main obstacles to the practical application of continuous-variable quantum key distribution (CVQKD). In this paper, we propose a multiplexing scheme to increase the secret key rate of the CVQKD system with orbital angular momentum (OAM). The propagation characteristics of a typical vortex beam, involving the Laguerre–Gaussian (LG) beam, are analyzed in an atmospheric channel for the Kolmogorov turbulence model. Discrete modulation is utilized to extend the maximal transmission distance. We show the effect of the transmittance of the beam over the turbulent channel on the secret key rate and the transmission distance. Numerical simulations indicate that the OAM multiplexing scheme can improve the performance of the CVQKD system and hence has potential use for practical high-rate quantum communications.     

基于光前置放大器的量子密钥分发融合经典通信方案

量子密钥分发融合经典通信方案将连续变量量子密钥分发和经典通信合并到了一起,为将来在现有的光网络上同时进行密钥分发和经典通信提供了一个有效的方法.然而,在量子信号上叠加一个经典信号将会给连续变量量子密钥分发系统引入过噪声从而大大降低系统的性能.本文提出基于光前置放大器的量子密钥分发融合经典通信方案,即在接收端插入光前置放...     

基于量子催化的离散调制连续变量量子密钥分发

相比于离散变量量子密钥分发,连续变量量子密钥分发虽然具备更高的安全码率等优势,但是在安全传输距离上却略有不足.尽管量子催化的运用对高斯调制连续变量量子密钥分发协议的性能,尤其在安全传输距离方面有着显著的提升,然而能否用来改善离散调制协议的性能却仍然未知.鉴于上述分析,本文提出了一种基于量子催化的离散调制协议的方案,试图在安全密钥率、安全传输距离和最大可容忍过噪声方面进一步提升协议性能.研究结果表明,在相同参数下,当优化量子催化引入的透射率T,相比于原始四态调制协议,所提方案能够有效地提升量子密钥分发的性能.特别是,对于可容忍过噪声为0.002,量子催化可将安全通信距离突破300 km,密钥率为10^-8bits/pulse,而过大的可容忍噪声会抑制量子催化对协议性能的改善效果.此外,为了彰显量子催化的优势,本文给出了点对点量子通信的最终极限Pirandola-Laurenza-Ottaviani-Banchi边界,仿真结果表明,虽然原始方案与所提方案都未能突破这种边界,但是相比于前者,后者能够在远距离通信上逼近于这种边界,这为实现全球量子安全通信的最终目标提供理论依据.     

Improving continuous-variable quantum key distribution under local oscillator intensity attack using entanglement in the middle

A modified continuous-variable quantum key distribution(CVQKD) protocol is proposed by originating the entangled source from a malicious third party Eve in the middle instead of generating it from the trustworthy Alice or Bob. This method is able to enhance the efficiency of the CVQKD scheme attacked by local oscillator(LO) intensity attack in terms of the generated secret key rate in quantum communication. The other indication of the improvement is that the maximum transmission distance and the maximum loss tolerance can be increased significantly, especially for CVQKD schemes based on homodyne detection.     

Parameter estimation of continuous variable quantum key distribution system via artificial neural networks

Continuous-variable quantum key distribution(CVQKD)allows legitimate parties to extract and exchange secret keys.However,the tradeoff between the secret key rate and the accuracy of parameter estimation still around the present CVQKD system.In this paper,we suggest an approach for parameter estimation of the CVQKD system via artificial neural networks(ANN),which can be merged in post-processing with less additional devices.The ANN-based training scheme,enables key prediction without exposing any raw key.Experimental results show that the error between the predicted values and the true ones is in a reasonable range.The CVQKD system can be improved in terms of the secret key rate and the parameter estimation,which involves less additional devices than the traditional CVQKD system.     

Counteracting a Saturation Attack in Continuous-Variable Quantum Key Distribution Using an Adjustable Optical Filter Embedded in Homodyne Detector

A saturation attack can be employed for compromising the practical security of continuous-variable quantum key distribution (CVQKD). In this paper, we suggest a countermeasure approach to resisting this attack by embedding an adjustable optical filter (AOF) in the CVQKD system. Numerical simulations illustrate the effects of the AOF-enabled countermeasure on the performance in terms of the secret key rate and transmission distance. The legal participants can trace back the information that has been eavesdropped by an attacker from the imperfect receiver, which indicates that this approach can be used for defeating a saturation attack in practical quantum communications.     

Simultaneous measurement-device-independent continuous variable quantum key distribution with realistic detector compensation

We propose a novel scheme for measurement-device-independent (MDI) continuous-variable quantum key distribution (CVQKD) by simultaneously conducting classical communication and QKD, which is called “simultaneous MDI-CVQKD” protocol. In such protocol, each sender (Alice, Bob) can superimpose random numbers for QKD on classical information by taking advantage of the same weak coherent pulse and an untrusted third party (Charlie) decodes it by using the same coherent detectors, which could be appealing in practice due to that multiple purposes can be realized by employing only single communication system. What is more, the proposed protocol is MDI, which is immune to all possible side-channel attacks on practical detectors. Security results illustrate that the simultaneous MDI-CVQKD protocol can secure against arbitrary collective attacks. In addition, we employ phasesensitive optical amplifiers to compensate the imperfection existing in practical detectors. With this technology, even common practical detectors can be used for detection through choosing a suitable optical amplifier gain. Furthermore, we also take the finite-size effect into consideration and show that the whole raw keys can be taken advantage of to generate the final secret key instead of sacrificing part of them for parameter estimation. Therefore, an enhanced performance of the simultaneous MDI-CVQKD protocol can be obtained in finite-size regime.     

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.     

Improving Continuous-Variable Quantum Key Distribution Using the Heralded Noiseless Linear Amplifier with Source in the Middle

We characterize the efficiency of the practical continuous-variable quantum key distribution (CVQKD) while inserting the heralded noiseless linear amplifier (NLA) before detectors to increase the secret key rate and the maximum transmission distance in Gaussian channels. In the heralded NLA-based CVQKD system, the entanglement source is only placed in the middle while the two participants are unnecessary to trust their source. The intensities of source noise are sensitive to the tunable NLA with the parameter g in a suitable range and can be stabilized to the suitable constant values to eliminate the impact of channel noise and defeat the potential attacks. Simulation results show that there is a well balance between the secret key rate and the maximum transmission distance with the tunable NLA.     

Continuous-Variable Quantum Key Distribution with Orthogonal Frequency Division Multiplexing Modulation

We demonstrate a multicarrier QKD protocol for continuous-variables (CV) using the orthogonal frequency division multiplexing (OFDM) technique which was employed in frequency domain. The multicarrier communication formulates sub-channels from OFDM technique and physical quantum channel, each dedicated to the transmission of a subcarrier CV. In the OFDM-CVQKD scenario, the input quantum states of the legal parties are granulated into subcarrier CVs, at the receiver, the subcarriers are decoded by an unitary CV operation, which results in the recovered single-carrier CVs. Compared with the device of the multichannel parallel CVQKD protocol that utilizes N arrayed-waveguide gratings (AWG) in optical domain, this protocol shows better feasibility of implementation from both equipment and technique. We derive the formulas of the secret key rate, moreover, analyze the security in the finite-size through the OFDM-CVQKD scheme. Simulation results indicate that the OFDM-CVQKD scheme leads to improved secret key rates and higher tolerable excess noise in comparison to single-carrier CVQKD. Particularly, the secret key rate of the 64 subcarrier CVQKD has increased by roughly an order of magnitude of the single-channel CVQKD, whereas the tolerable excess noise can be controlled in a small range. The results reveal that the OFDM-CVQKD protocol provides a feasible framework for the experimental implementation of an unconditionally secure communication over standard telecommunication networks.     

Four-State Continuous-Variable Quantum Key Distribution with Photon Subtraction

Four-state continuous-variable quantum key distribution (CVQKD) is one of the discretely modulated CVQKD which generates four nonorthogonal coherent states and exploits the sign of the measured quadrature of each state to encode information rather than uses the quadrature \(\hat {x}\) or \(\hat {p}\) itself. It has been proven that four-state CVQKD is more suitable than Gaussian modulated CVQKD in terms of transmission distance. In this paper, we propose an improved four-state CVQKD using an non-Gaussian operation, photon subtraction. A suitable photon-subtraction operation can be exploited to improve the maximal transmission of CVQKD in point-to-point quantum communication since it provides a method to enhance the performance of entanglement-based (EB) CVQKD. Photon subtraction not only can lengthen the maximal transmission distance by increasing the signal-to-noise rate but also can be easily implemented with existing technologies. Security analysis shows that the proposed scheme can lengthen the maximum transmission distance. Furthermore, by taking finite-size effect into account we obtain a tighter bound of the secure distance, which is more practical than that obtained in the asymptotic limit.     

Practical Analysis of Continuous-Variable Quantum Key Distribution Using a Nondeterministic Noiseless Linear Amplifier

We study the impact of the imperfections and the finite-size effect on the continuous-variable quantum key distribution (CVQKD) protocol with the nondeterministic noiseless linear amplifier (NLA). The imperfections of the homodyne detector and the imperfect amplification process as well as the finite-size effect on parameter estimation procedure are considered. We can see that despite the imperfections of the homodyne detector, the maximum improved transmission distance can still reach the equivalence of 20log₁₀g dB losses theoretically. Moreover, the analysis shows the imperfect amplification process of the NLA will slightly decrease the performance of the system. And we find the finite-size effect significantly influence the secret key rates of the NLA CVQKD protocol and the performance will approach the ideal asymptotic case with the increase of block size.     

Practical security analysis of continuous-variable quantum key distribution with an unbalanced heterodyne detector

When developing a practical continuous-variable quantum key distribution (CVQKD), the detector is necessary at the receiver's side. We investigate the practical security of the CVQKD system with an unbalanced heterodyne detector. The results show that unbalanced heterodyne detector introduces extra excess noise into the system and decreases the lower bound of the secret key rate without awareness of the legitimate communicators, which leaves loopholes for Eve to attack the system. In addition, we find that the secret key rate decreases more severely with the increase in the degree of imbalance and the excess noise induced by the imbalance is proportional to the intensity of the local oscillator (LO) under the same degree of imbalance. Finally, a countermeasure is proposed to resist these kinds of effects.     

The Improvement of Performance for Continuous-Variable Quantum Key Distribution with Imperfect Gaussian Modulation

Gaussian modulation is one of the key steps for the implementation of continuous-variable quantum key distribution (CVQKD) schemes. However, imperfection in the Gaussian modulation may introduce modulation noise that can deteriorate the performance of CVQKD systems. In this paper, we mainly investigate how to improve the performance of a CVQKD system from different aspects. First, we explore the several different origins, impacts and monitoring schemes for the modulation noise in detail. Then, we discuss the practical performance of a CVQKD system with an untrusted noise model and neutral party model, respectively. These analyses indicate that the neutral party model should be reasonably regarded as a general noise model, which will passively and greatly raise the performance of the system. Further, we propose a dynamic auto-bias control scheme to actively resist the modulation noise which comes from the drift of bias point of the amplitude modulator. Together these methods contribute to the improvement of the practical performance of CVQKD systems with imperfect Gaussian modulation.

     

Continuous-variable quantum key distribution based on photon addition operation

It is shown that the non-Gaussian operations can not only be used to prepare the nonclassical states, but also to improve the entanglement degree between Gaussian states. Thus these operations are naturally considered to enhance the performance of continuous variable quantum key distribution(CVQKD), in which the non-Gaussian operations are usually placed on the right-side of the entangled source. Here we propose another scheme for further improving the performance of CVQKD with the entangled-based scheme by operating photon-addition operation on the left-side of the entangled source.It is found that the photon-addition operation on the left-side presents both higher success probability and better secure key rate and transmission distance than the photon subtraction on the right-side, although they share the same maximal tolerable noise. In addition, compared to both photon subtraction and photon addition on the right-side, our scheme shows the best performance and the photon addition on the right-side is the worst.     

Analysis of atmospheric effects on the continuous variable quantum key distribution

Atmospheric effects have significant influence on the performance of a free-space optical continuous variable quantum key distribution (CVQKD) system. In this paper, we investigate how the transmittance, excess noise and interruption probability caused by atmospheric effects affect the secret-key rate (SKR) of the CVQKD. Three signal wavelengths, two weather conditions, two detection schemes, and two types of attacks are considered in our investigation. An expression aims at calculating the interruption probability is proposed based on the Kolmogorov spectrum model. The results show that a signal using long working wavelength can propagate much further than that of using short wavelength. Moreover, as the wavelength increases, the influence of interruption probability on the SKR becomes more significant, especially within a certain transmission distance. Therefore, interruption probability must be considered for CVQKD by using long-signal wavelengths. Furthermore, different detection schemes used by the receiver will result in different transmission distances when subjected to individual attacks and collective attacks, respectively.     

Polarization Attack on Continuous-Variable Quantum Key Distribution with a Local Local Oscillator

The estimation of phase noise of continuous-variable quantum key distribution protocol with a local local oscillator (LLO CVQKD), as a major process in quantifying the secret key rate, is closely relevant to the intensity of the phase reference. However, the transmission of the phase reference through the insecure quantum channel is prone to be exploited by the eavesdropper (Eve) to mount attacks. Here, we introduce a polarization attack scheme against the phase reference. Presently, in a practical LLO CVQKD system, only part of the phase reference pulses are measured to compensate for the polarization drift of the quantum signal pulses in a compensation cycle due to the limited polarization measurement rate, while the other part of the phase reference pulses are not measured. We show that Eve can control the phase noise by manipulating the polarization direction of the unmeasured phase reference to hide her attack on the quantum signal. Simulations show that Eve can obtain partial or total key rates information shared between Alice and Bob as the transmission distance increases. Improving the polarization measurement rate to 100% or monitoring the phase reference intensity in real-time is of great importance to protect the LLO CVQKD from polarization attack.     

Finite-size analysis of continuous-variable quantum key distribution with entanglement in the middle

Continuous-variable quantum key distribution(CVQKD) protocols with entanglement in the middle(EM) enable long maximal transmission distances for quantum communications. For the security analysis of the protocols, it is usually assumed that Eve performs collective Gaussian attacks and there is a lack of finite-size analysis of the protocols. However,in this paper we consider the finite-size regime of the EM-based CVQKD protocols by exposing the protocol to collective attacks and coherent attacks. We differentiate between the collective attacks and the coherent attacks while comparing asymptotic key rate and the key rate in the finite-size scenarios. Moreover, both symmetric and asymmetric configurations are collated in a contrastive analysis. As expected, the derived results in the finite-size scenarios are less useful than those acquired in the asymptotic regime. Nevertheless, we find that CVQKD with entanglement in the middle is capable of providing fully secure secret keys taking the finite-size effects into account with transmission distances of more than 30 km.