Performance improvement of eight-state continuous-variable quantum key distribution with an optical amplifier

Discrete modulation is proven to be beneficial to improving the performance of continuous-variable quantum key distribution (CVQKD) in long-distance transmission. In this paper, we suggest a construct to improve the maximal generated secret key rate of discretely modulated eight-state CVQKD using an optical amplifier (OA) with a slight cost of transmission distance. In the proposed scheme, an optical amplifier is exploited to compensate imperfection of Bob's apparatus, so that the generated secret key rate of eight-state protocol is enhanced. Specifically, we investigate two types of optical amplifiers, phase-insensitive amplifier (PIA) and phase-sensitive amplifier (PSA), and thereby obtain approximately equivalent improved performance for eight-state CVQKD system when applying these two different amplifiers. Numeric simulation shows that the proposed scheme can well improve the generated secret key rate of eight-state CVQKD in both asymptotic limit and finite-size regime. We also show that the proposed scheme can achieve the relatively high-rate transmission at long-distance communication 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.     

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.     

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.     

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.     

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.     

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.     

Phase Estimation and Compensation for Continuous-Variable Quantum Key Distribution

Phase estimation and compensation is one of the enabling functionalities in continous-variable quantum key distribution (CVQKD). Recently, a novel CVQKD scheme has been independently proposed to combat the local oscillator (LO) side channel attacks. Furthermore, we have carried out a proof-of-principle experimental study on the feasibility of the CVQKD without sending a LO. However, this scheme contains a serious weakness: The phase noise caused by the two different lasers between the sender and the receiver would severely destroy the quantum signal and finally reduce the secure distance. In this paper, we investigate the optical phase noise and explore the optimal approach to estimate and compensate such kind of noise with appropriate data overhead. Numerical simulations show that our scheme can successfully reconstruct the phase drifts even at low signal-to-noise ratio conditions. We also suggest that a higher accuracy of phase estimation could be achieved by using the frequency division multiplexing scheme. This opens an opportunity to employ advanced pilot-aided phase estimation techniques in quantum communication system.

     

Reference-frame-independent quantum key distribution of wavelength division multiplexing with multiple quantum channels

Reference-frame-independent quantum key distribution (RFI-QKD) can allow a quantum key distribution system to obtain the ideal key rate and transmission distance without reference system calibration, which has attracted much attention. Here, we propose an RFI-QKD protocol based on wavelength division multiplexing (WDM) considering finite-key analysis and crosstalk. The finite-key bound for RFI-QKD with decoy states is derived under the crosstalk of WDM. The resulting secret key rate of RFI-QKD, which is more rigorous, is obtained. Simulation results reveal that the secret key rate of RFI-QKD based on WDM is affected by the multiplexing channel number, as well as crosstalk between adjacent channels.     

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.     

Short-wave infrared continuous-variable quantum key distribution over satellite-to-submarine channels

The trans-media transmission of quantum pulse is one of means of free-space transmission which can be applied in continuous-variable quantum key distribution (CVQKD) system. In traditional implementations for atmospheric channels, the 1500-to-1600-nm pulse is regarded as an ideal quantum pulse carrier. However, the underwater transmission of this pulses tends to suffer from severe attenuation, which inevitably deteriorates the security of the whole CVQKD system. In this paper, we propose an alternative scheme for implementations of CVQKD over satellite-to-submarine channels. We estimate the parameters of the trans-media channels, involving atmosphere, sea surface and seawater and find that the short-wave infrared performs well in the above channels. The 450-nm pulse is used for generations of quantum signal carriers to accomplish quantum communications through atmosphere, sea surface and seawater channels. Numerical simulations show that the proposed scheme can achieve the transmission distance of 600 km. In addition, we demonstrate that non-Gaussian operations can further lengthen its maximal transmission distance, which contributes to the establishment of practical global quantum 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.     

A denial-of-service attack on fiber-based continuous-variable quantum key distribution

In a fiber-based continuous-variable quantum key distribution (CVQKD) system, to perform the channel estimation, the channel transmittance is usually assumed to be a constant. Subsequently, when the channel parameters are intentionally manipulated, the employed parameter estimation method will lead to deviations of channel parameters and ultimately impacting the evaluation of the secret key rate. In this paper, we propose a denial-of-service attack strategy based on Eve's manipulation of the channel parameters. In particular, we analyze in detail the impact of this attack when the channel transmittance is attacked and obeys two-point distribution and uniform distribution. The result shows that in both cases, Eve's slight manipulation on the quantum channel will lead to large underestimation of the secure transmission distance by using the previous parameter estimation, which will lead to intentional terminations of the communication. To prevent this attack, a simple data post-selection should be added before parameter estimation.     

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...     

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.     

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.     

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.     

Simultaneous two-way classical communication and measurement-device-independent quantum key distribution on oceanic quantum channels

Simultaneous two-way classical and quantum (STCQ) communication combines both continuous classical coherent optical communication and continuous-variable quantum key distribution (CV-QKD), which eliminates all detection-related imperfections by being measurement-device-independent (MDI). In this paper, we propose a protocol relying on STCQ communication on the oceanic quantum channel, in which the superposition-modulation-based coherent states depend on the information bits of both the secret key and the classical communication ciphertext. We analyse the encoding combination in classical communication and consider the probability distribution transmittance under seawater turbulence with various interference factors. Our numerical simulations of various practical scenarios demonstrate that the proposed protocol can simultaneously enable two-way classical communication and CV-MDI QKD with just a slight performance degradation transmission distance compared to the original CV-MDI QKD scheme. Moreover, the asymmetric situation outperforms the symmetric case in terms of transmission distance and optical modulation variance. We further take into consideration the impact of finite-size effects to illustrate the applicability of the proposed scheme in practical scenarios. The results show the feasibility of the underwater STCQ scheme, which contributes toward developing a global quantum communication network in free space.     

Temperature effects on atmospheric continuous-variable quantum key distribution

Compared with the fiber channel, the atmospheric channel offers the possibility of a broader geographical coverage and more flexible transmission for continuous-variable quantum key distribution(CVQKD). However, the fluctuation of atmospheric conditions will lead to the loss of performance in atmospheric quantum communication. In this paper, we study how temperature affects atmospheric CVQKD. We mainly consider the temperature effects on the transmittance and interruption probability. From the numerical simulation analysis, it can be shown that the performance of atmospheric CVQKD is improved as temperature increases, with the other factors fixed. Moreover, the results in this work can be used to evaluate the feasibility of the experimental implementation of the atmospheric CVQKD protocols.