Variable Quantum Key Distribution System Research Articles

Forced carrier perturbation opens a loophole for chip-based continuous variable quantum key distribution system

The integration of the continous-variable quantum key distribution(CVQKD) system is an important technical route with great potential value for constructing high-performance and low-cost CVQKD system. In all previous CVQKD studies, the quantum efficiency of the detector can be calibrated in advance and is considered to remain unchanged. But when the size of the system shrinks to the on-chip level, especially in the premise of non-uniform waveguide, heavy doping and other factors, effects such as free carrier absorption and scattering loss will become prominent, which will directly cause carriers undergo violent migration due to the tiny jitter of the local oscillator and further lead to dynamical variation of quantum efficiency of detection. In this paper, we propose a practical chip-based detector model, and numerous simulation results based on this model show that the practical system will face potential security threats due to the variable quantum efficiency. Moreover, two defense strategies are proposed to solve these practical security problems commonly exist in general chip-based CVQKD systems. This work breaks the inherent viewpoint that the quantum efficiency in the chip-based CVQKD system can still be calibrated in advance, and suggests a more rigorous consideration of practical security for development of chip-based CVQKD.

Underwater continuous variable quantum key distribution scheme based on imperfect measurement basis choice

Measurement basis choice is an essential step in the underwater continuous variable quantum key distribution system based on homodyne detection. However, in practice, finite bandwidth of analog-to-digital converter at the receiver’s side is limited, which can lead to defects in the measurement basis choice. That is, the receiver cannot accurately modulate the corresponding phase angle on the phase modulator for measurement basis choice to implement homodyne detection. The imperfect measurement basis choice will introduce extra excess noise, which affects the security of underwater continuous variable quantum key distribution scheme. To solve this problem, we propose an underwater continuous variable quantum key distribution scheme based on imperfect measurement basis choice, and analyze the impact of imperfect measurement basis choice on the performance of underwater continuous variable quantum key distribution system in detail. The research results indicate that the extra excess noise introduced by imperfect measurement basis choice can reduce the secret key rate and maximum transmission distance of the underwater Gaussian modulated quantum key distribution, thus reducing the security of the system. In order to achieve reliable underwater continuous variable quantum key distribution, we quantitatively analyze the extra excess noise introduced by the imperfect measurement basis choice and obtain its security limit. Besides, we also consider the influence of different seawater depths on the security limit of the proposed scheme, effectively solving the security risks caused by the imperfect measurement basis choice. Furthermore, for the proposed scheme, we not only consider its asymptotic security case but also its composable security case, and performance curves obtained in the latter are tighter than that achieved in the former. The proposed scheme aims to promote the practical process of underwater continuous variable quantum key distribution system and provide theoretical guidance for the accurate evaluation of water channel parameters in underwater communication of global quantum communication networks.

Research on dynamic polarization control in continuous variable quantum key distribution systems

In a commercial fiber-based quantum key distribution system, the local and signal optical fields are transmitted through long distance fibers by using time division multiplexing and polarization multiplexing. The state of polarization of the optical field is inevitably disturbed by random birefringence of the standard single-mode fiber caused by external complex environments. This drift of the state of polarization significantly affects the balanced homodyne detection results and the secret key rate. Therefore, the key technology of the dynamic polarization control unit is crucial for the system in a large-scale commercial application. We theoretically analyze and prove that the polarization control unit only needs the combination of two degrees of freedom when considering the result of an arbitrary polarization extinction ratio at the receiver of the system. To overcome the influence of polarization variations, we propose a chaotic monkey algorithm based on Bayesian parameter estimation method and implement intelligence algorithm on field programmable gate array (FPGA) hardware under pulsed light with an integral-type detector for the dynamic polarization control unit. The simulation results show that the optimal combination is four degrees of freedom and the optimal prior distribution is an exponential distribution among various distributions in the dynamic polarization control unit. According to the simulation results, the experimental results show that the achieved polarization extinction ratio is over 30 dB and the average time of polarization control is 400 μs for a single random polarization scrambling. By combining the dynamic polarization control unit with the system, we demonstrate the continuous variable quantum key distribution (CV-QKD) under a continuous polarization scrambling scope of 0－2 krad/s and verify its effectiveness. In addition, the methods presented will improve the performance of the system and expand the range of applications even under strong external disturbance.

Practical, high-speed Gaussian coherent state continuous variable quantum key distribution with real-time parameter monitoring, optimised slicing, and post-processed key distillation

Gaussian coherent state continuous variable quantum key distribution has gained interest owing to its security and compatibility with classical coherent optical fibre networks. For successful system deployment it is necessary to implement practical high speed systems which distil keys efficiently. Here, we demonstrate a Gaussian coherent state continuous variable quantum key distribution system at a 50 MHz symbol rate. Unlike most demonstrations to date which measure excess noise and infer key rates from this, we record signals in real time and distil keys. We also demonstrate, for the first time, slice reconciliation with optimised guard bands to maximise achievable secret key rates. Using this optimisation with multilevel slicing, a record 5 Mb/s secret key rate after a transmission distance of 25 km is achieved. This is a significant improvement on the 3 Mb/s secret key rate which is achieved with single level optimised slice reconciliation.

Robust frame synchronization for continuous-variable quantum key distribution with coherent states.

In a practical continuous variable quantum key distribution (CVQKD) system, frame synchronization is crucial for its operation, especially in conditions of low signal-to-noise ratio (SNR) and phase drift. This paper introduces a robust frame synchronization scheme for CVQKD systems that only utilizes quantum signals. The proposed scheme effectively employs randomly selected segments of quantum signals to achieve frame synchronization, eliminating the need for additional modulation. The performance of this scheme applied in a local local oscillator scenario is thoroughly analyzed through numerical simulations. The results demonstrate that the proposed scheme is capable of withstanding low SNR and arbitrary slow phase drift, as well as fast phase drift originates from two independent lasers, while also slightly improving the secret key rate compared to the scheme using inserted synchronization frames. These findings validate the feasibility of implementing the proposed scheme for long-distance CVQKD in practical scenarios.

Experimental demonstration of phase-sensitive multimode continuous variable quantum key distribution with improved secure key rate

We develop and experimentally demonstrate a phase-sensitive continuous variable quantum key distribution system with improved secure key rate. This is achieved using multimode coherent states with phase-conjugated subcarrier modulation and phase-sensitive detection. The local oscillator for phase-sensitive detection is regenerated from a polarization-multiplexed carrier wave via optical injection locking. The proposed scheme has a higher classical information capacity at a given number of received photons and exhibits a higher secure key rate when applying the security analysis of the GG02 protocol. Experimental results confirm the higher secret key rate and better excess noise tolerance of the new scheme compared to the typical implementation of GG02.

Denial-of-Service Attack Defense Strategy for Continuous Variable Quantum Key Distribution via Deep Learning

In the practical Continuous Variable Quantum Key Distribution (CVQKD) system, there is a large gap between the ideal theoretical model and the actual physical system. There are still some inevitable flaws, which give quantum hackers the opportunity to manipulate the channel in complex communication environments and launch Denial of Service attacks on the quantum channel. Therefore, a DoS attack-aware defense scheme for the CVQKD system based on convolutional neural networks (CNN) is proposed. The simulation results show that the proposed model can effectively detect DoS attacks launched by quantum hackers in CVQKD system in a complex communication environment, and the model has strong robustness due to the addition of the attention mechanism module. In addition, multiple sets of comparative experiments show that compared with the existing artificial neural network model, the CNN-based model has higher accuracy and stability.

MIMO Terahertz Quantum Key Distribution Under Restricted Eavesdropping

Quantum key distribution (QKD) can provide unconditional security to next generation communication networks guaranteed by the laws of quantum physics. This paper studies the secret key rate (SKR) of a continuous variable quantum key distribution (CV-QKD) system using multiple-input multipleoutput (MIMO) transmission and operating at Terahertz (THz) frequencies. Distinct from previous works, we consider a practical “restricted" eavesdropping scenario in which Eve can collect only a fraction of photons lost in the environment. We propose a system model for the MIMO THz CV-QKD system that accounts for restricted eavesdropping via a lossy wireless channel between Alice and Eve. We derive for this system new SKR expressions for both coherent-state-based and squeezed-state-based CV-QKD protocols. Our results show that previous analysis assuming unrestricted eavesdropping leads to overly pessimistic SKRs, and that in practice, the achievable SKR can be significantly increased under restricted eavesdropping. The increase in the SKR is quantified by the simplified SKR expansions derived in this paper. Our results also reveal that squeezing is beneficial for improving the SKR only for unrestricted eavesdropping. However, in a practical setting with restricted eavesdropping, increased squeezing leads to a reduction in the SKR.

Optimised Multithreaded CV-QKD Reconciliation for Global Quantum Networks

Designing a practical Continuous Variable (CV) Quantum Key Distribution (QKD) system requires an estimation of the quantum channel characteristics and the extraction of secure keys based on a large number of distributed quantum signals. On standard processors, it can take hours to reconcile the required number of quantum signals. This problem is exacerbated for Low Earth Orbit (LEO) satellite CV-QKD, where the satellite flyover time is less than a few minutes. A potential solution is massive parallelisation of the classical reconciliation where a large-code block is subdivided into many shorter blocks for individual decoding. However, the penalty of this procedure on the important final secured key rate is non-trivial to determine and hitherto has not been formally analysed. In this work, we fill this important knowledge gap via detailed analyses and experimental verification of a CV-QKD sliced reconciliation protocol that uses large block-length low-density parity-check decoders. Our new solution results in a significant increase in the final key rate relative to non-optimised reconciliation. In addition, it allows for the acquisition of quantum secured messages between terrestrial stations and LEO satellites within a flyover timescale even using off-the-shelf processors. Our work allows for optimised global quantum networks secured via fundamental physics.

Neural Network-Powered Nonlinear Compensation Framework for High-Speed Continuous Variable Quantum Key Distribution

In this paper, we present a neural network-based framework to compensate for the nonlinear distortion of high-speed continuous variable quantum key distribution (CV-QKD) systems. In practice, the nonlinear impairment of imperfect devices could bring interference to the measured quadrature values and thus compromise the parameter estimation procedure and the secure key rate. Specifically, for a high-speed CV-QKD system, the balanced homodyne detector (BHD) and the following analog-to-digital converter are the primary sources of nonlinear impairment. The nonlinear distortion effect will be more pronounced as the pulse repetition rate increases. We propose an autoencoder-based network to learn the inner patterns of distorted data and then compensate the quadrature measurements in real-time at the receiver’s side. The numerical simulation demonstrates that the excess noise induced by nonlinear impairment is reduced to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-3}$</tex-math></inline-formula> level in the shot noise unit. Consequently, such a software approach has the ability to significantly boost the bandwidth efficiency of the BHD and the secure key bit rate.

Channel Estimation and Secret Key Rate Analysis of MIMO Terahertz Quantum Key Distribution

We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.

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.

Simple security proofs for continuous variable quantum key distribution with intensity fluctuating sources

Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), the security has not been rigorously established for most current continuous variable quantum key distribution systems that have imperfections. Among these imperfections, intensity fluctuation is one of the principal problems affecting security. In this paper, we provide simple security proofs for continuous variable quantum key distribution systems with intensity fluctuating sources. Specifically, depending on device assumptions in the source, the imperfect systems are divided into two general cases for security proofs. In the most conservative case, we prove the security based on the tagging idea, which is a main technique for the security proof of discrete variable quantum key distribution. Our proofs are simple to implement without any hardware adjustment for current continuous variable quantum key distribution systems. Also, we show that our proofs are able to provide secure secret keys in the finite-size scenario.

The limits of multiplexing quantum and classical channels: Case study of a 2.5 GHz discrete variable quantum key distribution system

Network integration of quantum key distribution is crucial for its future widespread deployment due to the high cost of using optical fibers dedicated for the quantum channel only. We studied the performance of a system running a simplified BB84 protocol at 2.5 GHz repetition rate, operating in the original wavelength band, the short O-band, when multiplexed with communication channels in the conventional wavelength band, and the short C-band. Our system could successfully generate secret keys over a single-mode fiber with a length of 95.5 km and with co-propagating classical signals at a launch power of 8.9 dBm. Furthermore, we discuss the performance of an ideal system under the same conditions, showing the limits of what is possible with a discrete variable system in the O-band. We also considered a short and lossy link with 51 km optical fiber resembling a real link in a metropolitan area network. In this scenario, we could exchange a secret key with a launch power up to 16.7 dBm in the classical channels.

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.

Demonstration of high-speed and low-complexity continuous variable quantum key distribution system with local local oscillator

We present an experimental demonstration of the feasibility of the first 20 + Mb/s Gaussian modulated coherent state continuous variable quantum key distribution system with a locally generated local oscillator at the receiver (LLO-CVQKD). To increase the signal repetition rate, and hence the potential secure key rate, we equip our system with high-performance, wideband devices and design the components to support high repetition rate operation. We have successfully trialed the signal repetition rate as high as 500 MHz. To reduce the system complexity and correct for any phase shift during transmission, reference pulses are interleaved with quantum signals at Alice. Customized monitoring software has been developed, allowing all parameters to be controlled in real-time without any physical setup modification. We introduce a system-level noise model analysis at high bandwidth and propose a new ‘combined-optimization’ technique to optimize system parameters simultaneously to high precision. We use the measured excess noise, to predict that the system is capable of realizing a record 26.9 Mb/s key generation in the asymptotic regime over a 15 km signal mode fibre. We further demonstrate the potential for an even faster implementation.

Generation of −10.7 dB unbiased entangled states of light

In a continuous variable quantum key distribution (CV-QKD) system, strong Einstein–Podolsky–Rosen entangled states can significantly boost the robustness and distance for secure communication. However, an inevitable bias of two entanglement quadratures may degrade the secret key rate and distance during random quadrature base switching. The bias originates from several interdependent factors in the generation, propagation, and detection of entangled states, which faces a challenge to be completely eliminated. Here, we analyze in detail the origin of the bias effect and report on a scheme of generating unbiased entangled states, whereby a −10.7 ± 0.1 dB quadrature noise unbiased entanglement is first generated experimentally with two single-mode squeezed states. The unbiased quadrature correlations within the measurement bandwidth are expected to immensely enhance the key rate and secure distance for CV-QKD.

Phase locking and homodyne detection of repetitive laser pulses

A method to realize pulse laser phase locking and homodyne detection is proposed, which can be used in lidar and continuous variable quantum key distribution (CVQKD) systems. Theoretical analysis shows that homodyne detection of pulse laser has a sensitivity advantage of more than 4 dB over heterodyne detection. An experimental verification setup was constructed to realize phase-locking and homodyne detection of pulse lasers at repetition rates from 50 kHz to 2.4 MHz. For 320 ns signal laser pulses at 300 kHz with peak power of -65 dBm, the phase error is 8.9° (mainly limited by the chirp effect in the modulation of signal laser), and the detection signal-to-noise ratio reaches 20.2 dB. When the peak power is reduced to -75 dBm, phase locking and homodyne detection can still be achieved. Homodyne detection based on phase locking could serve as a novel weak-laser-pulse receiving method with high sensitivity and anti-interference performance.

Plug-and-play continuous-variable quantum key distribution for metropolitan networks.

We report a plug-and-play continuous variable quantum key distribution system (CV-QKD) with Gaussian modulated quadratures and a true local oscillator. The proposed configuration avoids the need for frequency locking two narrow line-width lasers. To minimize Rayleigh back-scattering, we utilize two independent fiber strands for the distribution of the laser and the transmission of the quantum signals. We further demonstrate the quantum-classical co-existing capability of our system by injecting high-power classical light in both fibers. A secret key rate up to 0.88 Mb/s is obtained by using two fiber links of 13 km and up to 0.3 Mb/s when adding 4 mW of classical light in the optical fiber used for transmitting the quantum signal. The reported performance indicates that the proposed QKD scheme has the potential to become an effective low-cost solution for metropolitan optical networks.

Performance of continuous variable quantum key distribution system at different detector bandwidth

We evaluate the performance of Gaussian Modulated Coherent State (GMCS) Continuous-Variable Quantum Key Distribution (CV-QKD), in terms of secure key rate, at different detector bandwidths. We illustrate the advantages and limitations of high-speed CV-QKD systems using a general noise model in which we consider various noise sources and their dependence upon detection bandwidth. Experimentally, the feasibility of high speed CV-QKD is demonstrated by using a GHz bandwidth balanced homodyne detector (BHD) established with commercially available components. We provide secure key rates of transmitted and local local oscillator schemes under various clock rates.