Discrete modulation continuous variable quantum key distribution under fast fading channel

A new method to quantify the eavesdropper's accessible information on continuous variable quantum key distribution for protocols implementing homodyne and heterodyne detections is introduced. We have derived upper bounds for the eavesdropping collective attacks on general continuous variable quantum key distribution protocols. Our focus is especially on deriving bounds which are Gaussian optimal for Eve collective attacks that involve non maximally entanglement (i.e. Alice and Bob use non maximally entangled states or non-Gaussian modulation for their quantum key distribution protocols). The new bounds derived are tight for all continuous variable quantum key distribution protocols. We show that the eavesdropper's accessible information is independent of the initial correlation between Alice and Bob modes in reverse reconciliation scheme, while in direct reconciliation scheme, Eve information is given as a function of Alice and Bob initial correlation.

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 on the receiver’s side is limited, which can result in 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 influence 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 choosing the imperfect measurement basis 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 consider not only its asymptotic security case but also its composable security case, and the 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 accurately evaluating the water channel parameters in underwater communication of global quantum communication networks.

Numerically, a theoretical analysis of the noise impact caused by spontaneous Raman scattering, four-wave mixing, and linear channel crosstalk on the measurement-device-independent continuous variable quantum key distribution systems is conducted. The analysis considers symmetry and asymmetry of system paths, as well as possible channel allocation schemes, for a quantum channel located in C-and O-bans. Mathematical models for MDI CV-QKD system and the contributing noises' description are provided. The secure key generation rate is estimated to state features of protocol operation when integrated with existing DWDM systems in the context of its implementation into telecommunication networks.

The Gaussian modulated continuous variable quantum key distribution (GM-CVQKD) protocol is known to maximise the mutual information between two parties during quantum key distribution (QKD). An alternative modulation scheme is the discrete modulated CVQKD (DM-CVQKD) protocol. In this paper, we perform a feasibility study for practical satellite-to-ground CVQKD with a focus on comparing existing GM-CVQKD and DM-CVQKD protocols with the application of the performance of recent reconciliation methods. We use a satellite-to-ground link model which takes into account geometric losses, scintillation, and scattering losses from the link distance, atmospheric turbulence, and atmospheric aerosols, respectively. In addition, recent multidimensional (MD) and multilevel coding and multistage decoding (MLC-MSD) reconciliation method models in combination with multiedge-type low-density parity-check (MET-LDPC) code models have been used to determine the reconciliation efficiency. Realistic parameters have been used for the calculation of the secret key rate (SKR) along with a comparison between MD and MLC-MSD reconciliation during satellite-to-ground GM-CVQKD, for the first time. The results show that GM-CVQKD outperforms DM-CVQKD. In addition, GM-CVQKD with MD reconciliation outperforms GM-CVQKD with MLC-MSD reconciliation in the finite size limit by producing positive SKRs at larger link distances and lower elevation angles.

The distribution of deterministic keys is of significance in personal communications, but the existing continuous variable quantum key distribution protocols can only generate random keys. By exploiting the entanglement properties of two-mode squeezed states, a continuous variable quantum deterministic key distribution (CVQDKD) scheme is presented for handing over the pre-determined key to the intended receiver. The security of the CVQDKD scheme is analyzed in detail from the perspective of information theory. It shows that the scheme can securely and effectively transfer pre-determined keys under ideal conditions. The proposed scheme can resist both the entanglement and beam splitter attacks under a relatively high channel transmission efficiency.

Continuous variable quantum key distribution (CV-QKD) has emerged as a promising candidate for quantum-secure communication due to its experimentally demonstrated high key rates in fiber-optic channels. However, the feasibility of discrete modulation CV-QKD in satellite-to-ground downlinks remains an open question due to practical challenges such as high transmission loss, limited communication windows, and atmospheric turbulence. In this work, a comprehensive framework is proposed to evaluate the feasibility of discrete modulation CV-QKD by integrating orbital dynamics and atmospheric channel models, and to comprehensively analyze the influence of the parameter space on free-space discrete modulation CV-QKD. To achieve this, a free-space CV-QKD simulation platform is employed, which calculates the elevation angle and transmission distance based on precise orbital models, thereby providing a more practical assessment of the key rate for discrete modulation CV-QKD. Simulation results verify the feasibility and practicality of discrete modulation CV-QKD in satellite-based quantum communication systems. Furthermore, the critical factors influencing the key rate performance are identified, and parameter optimization strategies are proposed, providing theoretical support for realizing the future satellite-to-ground discrete modulation CV-QKD.

We study the validity of partially trusting the phase noise associated with estimation uncertainty in a continuous variable quantum key distribution system with a local local oscillator (LLO-CVQKD) and investigate optimal system parameters. We find that the trusted phase noise model enhances the key rate and transmission distance performance but opens a security loophole by manipulating the reference pulse amplitude. Therefore, we propose a “reference pulse attack” on the trusted phase noise LLO-CVQKD system where Eve achieves 100% information hacking without being detected at 23.8km and 32.0km while using lossless and 0.14dB/km loss channels, respectively. Nevertheless, by re-analyzing the attack, countermeasures are also proposed to keep the performance advantages of the trusted phase noise model. As a result, the trusted phase noise LLO-CVQKD can still provide a superior secure key rate (e.g., 9 times higher key rate at 20km) and an increased transmission distance by 45%, compared to that of the untrusted phase noise system.

High relative velocities and large distances in space-based quantum communication with satellites in lower earth orbits can lead to significant Doppler shifts and delays of the signal impairing the achievable performance if uncorrected. We analyze the influence of systematic and stochastic Doppler shift and delay in the specific case of a continuous variable quantum key distribution (CV-QKD) protocol and identify the generalized correlation function, the ambiguity function, as a decisive measure of performance loss. Investigating the generalized correlations as well as private capacity bounds for specific choices of spectral amplitude shape (Gaussian, single- and double-sided Lorentzian), we find that this choice has a significant impact on the robustness of the quantum communication protocol to spectral and temporal synchronization errors. We conclude that optimizing the pulse shape can be a building block in the resilient design of quantum network infrastructure.

Continuous variable quantum key distribution (CVQKD) is a developing method to secure information exchange in future quantum networks. With the recent developments in quantum technology and greater access to space, a global quantum network secured by CVQKD can be within reach. In this work, the structures of existing QKD networks are analyzed, and how they can be fit into a general overarching three‐layer QKD network architecture for the endeavor of a global QKD network. Such a network can comprise different links in fiber and free‐space. The finite size limit secret key rates (SKRs) with multidimensional reconciliation are calculated for the different links for which CVQKD can be used in such a network. The results show that CVQKD generally achieves longer distances and larger SKRs in inter‐satellite, satellite‐to‐ground, fiber, and underwater links in descending order. The different links and nodes are classified and secret key distribution is studied as a graph problem. The link capacity, a routing metric for secret key distribution, which considers a dynamic SKR based on dynamic links is presented. Its use in simulated CVQKD networks is presented for the aim of spatiotemporal secret key distribution through a dynamic CVQKD network.

We prove security against collective attacks of a four-state discretely signaled continuous variable quantum key distribution protocol with and without post-selection. This protocol is compatible with optical networks and high speed coding techniques.

Continuous variable quantum key distribution (CVQKD) based on a simultaneous quantum and classical communication (SQCC) protocol can use a single coherent communication system for multiple purposes. In this paper, we propose an inter-satellite SQCC-CVQKD scheme in the terahertz (THz) band. This scheme performs classical modulation at the sending end, followed by quantum Gaussian modulation operations. At the receiving end, an amplifier is used to amplify and demultiplex the received signal, and, finally, a homodyne detector or heterodyne detector is selected for decoding. We have demonstrated the security of the SQCC-CVQKD system in the THz band, and a performance analysis of the scheme is given in the finite-size regime. The simulation results show that this scheme has a higher secret key rate and stronger anti-interference ability in practice. This work provides an effective way to construct wireless quantum communication networks.

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.

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.

Continuous variable quantum key distribution (CV-QKD) allows the distribution of symmetric keys in a secure manner. CV-QKD systems can extract keys at its maximum rate when using Gaussian modulation (GM). Nonetheless, GM demands high-capacity random number sources and tends to be very hard to approach in practice. To circumvent these disadvantages, higher-order probabilistic -shaped discrete modulation (DM) can be used. State-of-the-art works compute the key rates of DM-CV-QKD systems considering a fixed value for the reconciliation efficiency and do not take into account the frame error rate (FER) of the system, thus over or under estimating the key rates. In this work, we study the security bounds of CV-QKD systems considering probabilistic shaped DM formats with 256-symbols in the finite-size regime. This accounting for the true value of the reconciliation efficiency, and the FER of the information reconciliation step. Both conventional and hexagonal 256-quadrature amplitude modulation (QAM) constellations yield higher key rates than 256-amplitude and phase shift keying (APSK) constellations, with 256-QAM constellations being indistinguishable in performance with GM for high transmission distances. Minimum signal-to-noise ratio (SNR) values were fixed from a FER analysis through a CV-QKD simulation allowing for key extraction considering different FER levels. Lower FER values are associated with higher SNRs in the system and thus lower achievable transmission distances. Nonetheless, the FER maximizing the extraction key rate is not null. Our results show that the extraction key rate is maximized by SNR adjustment which should have in account both the reconciliation efficiency and the FER.

An efficient and practical post-processing technique based on reverse reconciliation for continuous variable quantum key distribution is proposed and simulated with low-density parity check (LDPC) codes. MultiLevel Coding/MultiStage Decoding, which fully utilizes optimization technique such as vector quantization and iterative decoding and the optimal channel coding most close to the Shannon limit, was used to realize efficient reverse reconciliation algorithm. Simulation results showed that the proposed method can improve the secure key distribution rate to 2.2 kb/s and the coding efficiency to 0.89 over 20 km in single-mode optical fiber. Moreover, there still is room for much improvement.