Continuous-variable Quantum Key Distribution Protocol Research Articles

Mapping Guaranteed Positive Secret Key Rates for Continuous Variable Quantum Key Distribution.

The standard way to measure the performance of existing continuous variable quantum key distribution (CVQKD) protocols is by using the achievable secret key rate (SKR) with respect to one parameter while keeping all other parameters constant. However, this atomistic method requires many individual parameter analyses while overlooking the co-dependence of other parameters. In this work, a numerical tool is developed for comparing different CVQKD protocols while taking into account the simultaneous effects of multiple CVQKD parameters on the capability of protocols to produce positive SKRs. Using the transmittance, excess noise, and modulation amplitude parameter space, regions of positive SKR are identified to compare three discrete modulated (DM) CVQKD protocols. The results show that the M-QAM protocol outperforms the M-APSK and M-PSK protocols and that there is a non-linear increase in the capability to produce positive SKRs as the number of coherent states used for a protocol increases. The tool developed is beneficial for choosing the optimum protocol in unstable channels, such as free space, where the transmittance and excess noise fluctuate, providing a more holistic assessment of a protocol's capability to produce positive SKRs.

Enhancing Performance of Continuous-Variable Quantum Key Distribution (CV-QKD) and Gaussian Modulation of Coherent States (GMCS) in Free-Space Channels under Individual Attacks with Phase-Sensitive Amplifier (PSA) and Homodyne Detection (HD).

In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.

Passive continuous-variable quantum key distribution based on orthogonal frequency-division multiplexing in the terahertz band

We propose a passive continuous-variable quantum key distribution protocol based on multicarrier multiplexing technology in the terahertz band. In this paper, we realize the superposition of multipath coherent states by inverse Fourier transform and passive modulation. At the receiving end, the coherent states of the subcarriers are separated by quantum Fourier transform, and the keys are obtained in parallel by a homodyne (heterodyne) detector and post-processing. In addition, we derive the security bounds of the protocol and evaluate the performance in indoor environments and intersatellite links. Furthermore, we consider finite-size effects and propose tighter agreement constraints, which are more practical than those obtained in the asymptotic limit. This work will provide an effective way to build efficient wireless quantum communication networks.

Underwater Wavelength Attack on Discrete Modulated Continuous-Variable Quantum Key Distribution.

The wavelength attack utilizes the dependence of beam splitters (BSs) on wavelength to cause legitimate users Alice and Bob to underestimate their excess noise so that Eve can steal more secret keys without being detected. Recently, the wavelength attack on Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) has been researched in both fiber and atmospheric channels. However, the wavelength attack may also pose a threat to the case of ocean turbulent channels, which are vital for the secure communication of both ocean sensor networks and submarines. In this work, we propose two wavelength attack schemes on underwater discrete modulated (DM) CV-QKD protocol, which is effective for the case with and without local oscillator (LO) intensity monitor, respectively. In terms of the transmittance properties of the fused biconical taper (FBT) BS, two sets of wavelengths are determined for Eve's pulse manipulation, which are all located in the so-called blue-green band. The derived successful criterion shows that both attack schemes can control the estimated excess noise of Alice and Bob close to zero by selecting the corresponding condition parameters based on channel transmittance. Additionally, our numerical analysis shows that Eve can steal more bits when the wavelength attack controls the value of the estimated excess noise closer to zero.

Error correction based artificial neural network in multi-modes CV-QKD with simultaneous type-I and type-II parametric-down conversion entangled photon source

We model simultaneous type-I and type-II phase matching in a single non-linear crystal (NLC), based on a double periodically poled lithium niobate crystal. We also discuss entanglement based continuous variable quantum key distribution (CV-QKD), and the security of such scheme is analyzed considering an eavesdropper being capable of individual attacks. We further demonstrate efficiency of the artificial neural network (ANN) algorithm during post-processing or errors correction in such CV-QKD protocols. Results show that employing simultaneous type-I and type-II SPDC process in single NLC is a potential source to generate high dimensional (or hyper-entangled) states, strongly required for quantum information processing tasks, an example of CV-QKD. Security analysis of such a CV-QKD protocol shows a strong advantage of employing the above entangled photon state source, given that it provides a higher secure key rate and thus a secure communication within a larger distance. In addition, the suggested error correction algorithm is less time consuming and highly efficient, since full synchronization is achieved just after a few number of updates of trusted parties’ tree-parity-machines. Our results sufficiently demonstrate that the suggested CV-QKD is able to distribute secure keys in nearby inter-city areas, and therefore allows lower-cost secure communication networks.

Phase compensation of a continuous-variable quantum key distribution via temporal convolutional neural network

Abstract Although the continuous-variable quantum key distribution (CV-QKD) protocol based on a local local oscillator (LLO) can close all the security loopholes from the transmitted local oscillator (TLO), the phase noise caused by the inaccurate phase reference information limits the performance of the protocol. To reduce the residual phase noise, in this work, we propose a phase estimation and compensation method based on the temporal convolutional neural (TCN) model, where a part of phase information obtained by measuring pilot pulses is employed as the training data and input into the TCN module. With a trained TCN module, the subsequent phase drifts can be more accurately estimated, allowing for better phase compensation and lower phase noise. Numerical analysis shows that the proposed scheme can improve the transmission distance and the secret key rate of the LLO protocol.

Classical-quantum dual encoding for laser communications in space

In typical laser communications classical information is encoded by modulating the amplitude of the laser beam and measured via direct detection. We add a layer of security using quantum physics to this standard scheme, applicable to free-space channels. We consider a simultaneous classical-quantum communication scheme where the classical information is encoded in the usual way and the quantum information is encoded as fluctuations of a sub-Poissonian noise-floor. For secret key generation, we consider a continuous-variable quantum key distribution protocol (CVQKD) using a Gaussian ensemble of squeezed states and direct detection. Under the assumption of passive attacks secure key generation and classical communication can proceed simultaneously. Compared with standard CVQKD, which is secure against unrestricted attacks, our added layer of quantum security is simple to implement, robust and does not affect classical data rates. We perform detailed simulations of the performance of the protocol for a free-space atmospheric channel. We analyse security of the CVQKD protocol in the composable finite-size regime.

Four-state continuous variable quantum key distribution with two accelerating partners

The field of quantum communication has gradually expanded to include satellites in Earth's orbit. However, for long-distance communication protocols, gravity and its effect on quantum states must be taken into account. By applying the equivalence principle, we can consider that the gravitational effects are equivalent to the acceleration that observers possess. A comprehensive method is proposed to find out the effect of gravity on the performance of the four-state continuous-variable quantum key distribution (CV-QKD) protocol. Finally, the effects of gravity on the QKD of each protocol are discussed, and the associated factors are also analyzed. The performance of the CV-QKD protocol under the effects of gravity is deeply analyzed by taking acceleration into consideration. Both the asymptotic key rate and the finite-size key rate are analyzed in this paper. Furthermore, significant room exists for improving the security and efficiency of space quantum communication.

Robustness of entanglement-based discrete- and continuous-variable quantum key distribution against channel noise

Discrete-variable (DV) and continuous-variable (CV) schemes constitute the two major families of quantum key distribution (QKD) protocols. Unfortunately, since the setup elements required by these schemes are quite different, making a fair comparison of their potential performance in particular applications is often troublesome, limiting the experimenters’ capability to choose an optimal solution. In this work we perform a general comparison of the major entanglement-based DV and CV QKD protocols in terms of their resistance to the channel noise, with the otherwise perfect setup, showing the definite superiority of the DV family. We analytically derive fundamental bounds on the tolerable channel noise and attenuation for entanglement-based CV QKD protocols. We also investigate the influence of DV QKD setup imperfections on the obtained results in order to determine benchmarks for the parameters of realistic photon sources and detectors, allowing the realistic DV protocols to outperform even the ideal CV QKD analogs. Our results indicate the realistic advantage of DV entanglement-based schemes over their CV counterparts and suggests the practical efforts for maximizing this advantage.

Generating local oscillator locally in continuous variable quantum key distribution using optical injection phase locked loop: a theoretical approach.

In this study, we investigate the feasibility of utilizing optical injection locking with phase-locked loop feedback to generate a true local oscillator for continuous-variable quantum key distribution (CV-QKD). We evaluate the noise and imperfections associated with this novel approach and compare our findings with existing CV-QKD schemes. Notably, our calculations demonstrate significantly lower noise levels compared to other locally generated local oscillator-based CV-QKD schemes. Furthermore, we assess the secure key rate and achievable distance under collective attack for our proposed scheme and compare it to other variants of CV-QKD protocols employing a true local oscillator. Our results align well with experimental data, highlighting the promise of our approach.

A Survey of Machine Learning Assisted Continuous-Variable Quantum Key Distribution

Continuous-variable quantum key distribution (CV-QKD) shows potential for the rapid development of an information-theoretic secure global communication network; however, the complexities of CV-QKD implementation remain a restrictive factor. Machine learning (ML) has recently shown promise in alleviating these complexities. ML has been applied to almost every stage of CV-QKD protocols, including ML-assisted phase error estimation, excess noise estimation, state discrimination, parameter estimation and optimization, key sifting, information reconciliation, and key rate estimation. This survey provides a comprehensive analysis of the current literature on ML-assisted CV-QKD. In addition, the survey compares the ML algorithms assisting CV-QKD with the traditional algorithms they aim to augment, as well as providing recommendations for future directions for ML-assisted CV-QKD research.

Simultaneous continuous-variable quantum key distribution and classical optical communication over a shared infrastructure

Integrating quantum key distribution (QKD) and classical optical communication for large-scale applications presents a significant challenge due to high cost and complexity. In this paper, we experimentally demonstrate the feasibility of simultaneous continuous-variable QKD (CV-QKD) and classical optical communication over a shared infrastructure. Through high-linearity modulators and detectors, we validated classical quadrature phase shift keying communication and CV-QKD protocol on a single platform by time-division multiplexing technology. Experimental results show that the classical communication achieved a bit rate of 200 Mbits/s, and the CV-QKD protocol achieved a secret key rate of 1.12 Mbits/s at 6 dB channel attenuation. This work reveals the feasibility of using a shared optical module to realize classical and quantum communication, leading to simplified integrating QKD and classical communication infrastructure.

Optimizing state-discrimination receivers for continuous-variable quantum key distribution over a wiretap channel

We address a continuous-variable quantum key distribution protocol employing quaternary phase-shift-keying of coherent states and a non-Gaussian measurement inspired by quantum receivers minimizing the error probability in a quantum-state-discrimination scenario. We consider a pure-loss quantum wiretap channel, in which a possible eavesdropper is limited to collect the sole channel losses. We perform a characterization of state-discrimination receivers and design an optimized receiver maximizing the asymptotic secure key rate (SKR), namely the key-rate optimized receiver (KOR), comparing its performance with respect to the pretty good measurement and the heterodyne-based protocol. We show that the KOR increases the SKR for metropolitan-network distances. Finally, we also investigate the implementations of feasible schemes, such as the displacement feed-forward receiver, obtaining an increase in the SKR in particular regimes.

Experimental realization of free-space continuous-variable quantum key distribution based on fiber Sagnac interferometer.

The Gaussian-modulated coherent state (GMCS) is a well-known continuous-variable quantum key distribution (CV-QKD) protocol that is robust to incoherent background noise and can effectively suppress ambient light in free space. However, it is difficult to implement this protocol in free space using existing polarization coding schemes. In this Letter, we propose a polarization coding structure based on a self-compensating fiber Sagnac interferometer, which can reduce the required modulation voltage by two orders of magnitude and achieve fast and arbitrary polarization modulation, and experimentally demonstrate polarization coding-based GMCS CV-QKD for, it is believed, the first time. The proposed polarization modulation structure, which uses off-the-shelf fiber components, is compact, simple, and suitable for mobile terminals, such as flying lifts.

Suppression of Fading Noise in Satellite-Mediated Continuous-Variable Quantum Key Distribution via Clusterization

The satellite-mediated continuous-variable quantum key distribution (CV-QKD) protocol, which relies on off-the-shelf telecommunication components, has the potential for a global quantum communication network with all-day operation. However, the transmittance fluctuation of satellite-mediated links leads to the arriving quantum state showing non-Gaussian property, introducing extra fading noise in security analysis and limiting the secret key rate of the protocol. Here, we consider the clusterization method for data post-processing to suppress the fading noise in both downlink and uplink scenarios, where the measurement data are divided into several clusters, and we perform security analysis separately. In particular, we set the optimal upper and lower bounds of each cluster in terms of the probability distribution of transmittance (PDT), while finding an optimal cluster number for the trade-off between fading noise and the composable finite-size effect. Numerical analysis shows that the proposed method can improve the composable finite-size rate when the fading noise is large enough, even with only two clusters. Moreover, a high-speed CV-QKD system with a higher frequency of signal preparation and detection can extend the proposed method to work in the case of lower fading noise.

Experimental free-space continuous-variable quantum key distribution with thermal source.

Passive-state-preparation (PSP) continuous-variable quantum key distribution (CVQKD) protocol explores the intrinsic field fluctuations of a thermal source. Compared with traditional Gaussian-modulated coherent-state CVQKD, it does not need active modulations and has promising applications in chip integration and portable free-space quantum key distribution. In this Letter, we propose and experimentally realize a PSP CVQKD scheme with transmitted local oscillator (LO) through fluctuating transmittance free-space channel using an off-the-shelf amplified spontaneous emission source for the first time. By proposing thermal-state polarization multiplexing transmitted LO, synchronized channel transmittance monitoring and fine-grained phase compensation techniques, secure keys within -15 dB transmittance of simulated free-space channel with turbulence are generated, with a final average secure key rate of 1.015 Mbps asymptotically. Equivalent atmospheric turbulence model analysis shows that the free-space PSP CVQKD scheme provides a promising outlook for high-speed and chip-based CVQKD for kilometer-level atmospheric channel networks.

Small-form-factor Gaussian-modulated coherent-state transmitter for CV-QKD using a gain-switched DFB laser.

We report a directly modulated distributed feedback laser operating in gain-switching mode for preparing the coherent states required for the Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) protocol. The proposed single-component quantum transmitter design eliminates the need for external modulators, decreasing the complexity of GMCS CV-QKD systems. The experimental results demonstrate a potential asymptotic secret key rate value of 2.63 Mbps over an 11-km fiber link, making the directly modulated GMCS transmitter particularly suitable for metropolitan optical networks where compactness, robustness, and low cost are key desirable features.

Security against Collective Attacks for a Continuous-Variable Quantum Key Distribution Protocol Using Homodyne Detection and Postselection

We analyze the security against collective attacks for a homodyne-based continuous-variable quantum key distribution protocol using binary coherent states and postselection. We derive a lower bound of the secret key rate in an asymptotic scenario, and numerically optimize it for the case of a symmetric Gaussian channel.

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.

Quantum Key Distribution Using a Single-Photon Added–Subtracted Squeezed Coherent State

We investigate the security of continuous-variable BB84 quantum key distribution protocol using a single-photon added and then subtracted squeezed coherent state (SPASSCS). We find that the SPASSCS is a non-Gaussian and nonclassical state; its non-Gaussianity and nonclassicality are exhibited through the Wigner function. We show that the proposed state is generally robust against the eavesdropping strategies, such as intercept-resend attack and superior channel attack. Further, a comparative study proves the strong efficiency of the proposed state over the coherent state, squeezed coherent state and photon-added then subtracted coherent state. In our analysis, we employ bit error rate, mutual information, and secure key gain.